Valeria Fanghella
email: valeria.fanghella@grenoble-em.com

Lisette Ibanez
email: lisette.ibanez@inrae.fr

John Thøgersen

"What you don't know, can't hurt you": Self-image motivation in charitable giving

Keywords: dictator game, opt-out option, self-image, charitable giving, social information. JEL classification: C90, D91

published or not. The documents may come

Introduction

Prosocial behavior, a fundamental aspect of human social interactions, is often intertwined with a paradox. While people frequently behave prosocially, they also have a propensity to avoid situations that call for prosocial behavior. This propensity manifests in a multitude of real-world contexts-such as walking away from solicitors [START_REF] Andreoni | Avoiding the ask: A field experiment on altruism, empathy, and charitable giving[END_REF][START_REF] Trachtman | Fair weather avoidance: unpacking the costs and benefits of "Avoiding the Ask[END_REF] or refusing to open the door to them [START_REF] Dellavigna | Testing for Altruism and Social Pressure in Charitable Giving[END_REF]. Laboratory studies have also revealed that some individuals pay to quietly exit a dictator game (DG), forgoing an obvious gain (e.g., [START_REF] Broberg | Is generosity involuntary?[END_REF][START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF][START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF][START_REF] Lazear | Sorting in Experiments with Application to Social Preferences[END_REF]. A recurring element of these studies is the presence of social interactions, such as with a solicitor making a donation request or with a recipient awaiting the offer of a dictator. Within these contexts, individuals' donations may be motivated by a desire to meet others' expectations and to signal to others that they are altruistic. Hence, avoiding the request becomes a strategy for pursuing self-interest while upholding a positive social image.

This study departs from the existing literature by focusing on self-image as a driver for avoiding prosocial requests. Self-image motivation differs from social image motivation, as it revolves around individuals' motivation to behave prosocially to signal to themselves (rather than to others) that they are altruistic [START_REF] Bénabou | Identity, morals, and taboos: Beliefs as assets[END_REF].

To investigate this, we conducted a pre-registered, incentivized online experiment (N = 1400), where participants played two consecutive DGs with a charity. In the first stage, we varied the type of DG and the information provided to participants with a 2×2 between-subjects design: (i) standard DG or DG with a costly opt-out; (ii) with or without social information (about mean donation by participants in a previous session, including non-donors). The first factor captured the propensity to avoid a donation request, with the DG with the costly opt-out (from here on, we omit "costly") allowing participants to renounce a fixed part of their endowment to avoid playing the DG [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF].

The second factor was aimed at studying the interplay between self-image motivation and social information. Notably, it allowed us to investigate whether exposure to others' good behavior increases the probability of avoiding the game, as social information may create a feeling of obligation to comply with others' behavior to maintain a positive self-image. The second stage involved a standard DG for all participants, which measured temporal dynamics by distinguishing for the motivation to donate in the first decision.

Our design is ideal for studying the effect of self-image motivation on the decision to avoid a donation request. The recipient, a charity, is unaware of the existence of the experiment and of the source of the donation. Thus, it cannot be disappointed by a low donation or interpret a donation as a signal of participant's altruism. Furthermore, decisions are anonymous, meaning that a participant is the sole audience for their own behavior [START_REF] Tonin | Experimental evidence of self-image concerns as motivation for giving[END_REF]. Opting out can thus only be explained by self-image motivation, which allows participants to "overlook" the donation request and maintain a positive view of themselves even without donating [START_REF] Adena | Online fundraising, self-image, and the long-term impact of ask avoidance[END_REF].

Our study contributes to the literature in three ways. First, we delve into the phenomenon of avoiding prosocial requests in the absence of social interactions. In this situation, opting out is driven by the desire to maintain one's self-image while behaving selfishly. Importantly, we make the opt-out option costly, allowing us to assess the strength of self-image motivation. When the opt-out option is free, participants face no cost while potentially gaining benefits from opting out, making it an appealing choice. Our design allows us to determine whether self-image motivation is strong enough that participants would pay to avoid the donation request. [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF] indicate that when opting out is costly and social expectations are absent, barely any dictators opt out. On the other hand, the two studies we are aware of that have observed opting out without social interactions both included a free opt-out option [START_REF] Adena | Online fundraising, self-image, and the long-term impact of ask avoidance[END_REF][START_REF] Tonin | Experimental evidence of self-image concerns as motivation for giving[END_REF].

Second, we explore the interplay between self-image motivation and social information. While social information is often used to encourage prosocial (e.g., [START_REF] Agerström | Using descriptive social norms to increase charitable giving: The power of local norms[END_REF][START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF][START_REF] Shang | A Field Experiment in Charitable Contribution: The Impact of Social Information on the Voluntary Provision of Public Goods[END_REF] and pro-environmental [START_REF] Andor | Behavioral Economics and Energy Conservation -A Systematic Review of Non-price Interventions and Their Causal Effects[END_REF][START_REF] Farrow | Social Norms and Pro-environmental Behavior: A Review of the Evidence[END_REF] behavior, recent research indicates that it may create disutility among non-compliers [START_REF] Allcott | The welfare effects of nudges: A case study of energy use social comparisons[END_REF]. Preliminary evidence in line with such an interplay between self-image and social information is put forward by [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF]. The author shows that when high descriptive norms (previous donation by one participant) are presented before the decision on whether to donate, they increase the number of free opt-outs. According to Klinowski, this result occurs because opting out becomes socially acceptable when others have already made large donations. In this interpretation, opting out is not driven by the need to conform to others' behavior to maintain a positive self-image; instead, knowing that others behave prosocially frees individuals from feeling compelled to do the same.

Our study differs from that of Klinowsky (2020) by focusing on social information in the form of a descriptive norm (mean donation by participants in a previous session, including non-donors) and making the opt-out option costly. As [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF], we also predict an increase in opt-outs when social information is provided, but through a different mechanism. We propose that, in order to maintain a positive self-image, participants may feel that they have to comply with others' behaviors.

Consequently, participants primarily driven by self-image motivation, who originally intended to contribute an amount below the descriptive norm, may opt out to avoid a negative self-image arising from donating less than others. In this view, social information is potentially utility-reducing (as in [START_REF] Allcott | The welfare effects of nudges: A case study of energy use social comparisons[END_REF]. Third, we explore the impact of self-image motivation on a subsequent donation request. In doing so, our research introduces a novel perspective to the literature on temporal dynamics of prosocial behavior (e.g., [START_REF] Brañas-Garza | Moral cleansing and moral licenses: Experimental evidence[END_REF][START_REF] Dolan | Like ripples on a pond Behavioral spillovers and their implications for research and policy[END_REF][START_REF] Schmitz | Temporal dynamics of pro-social behavior: an experimental analysis[END_REF], shedding light on why these dynamics may vary among individuals.

The remainder of the paper proceeds as follows. In Sections 2 and 3, we describe the pre-registered experimental design and behavioral predictions, respectively. Section 4 presents the results, followed by Section 5, which discusses the main findings and concludes.

Materials and methods

Participants and procedure

We conducted the experiment on the online platform Prolific in January 2022. To prevent the description of the study from affecting self-selection into participation, it was presented as a general study on decision-making. First, participants gave consent and were informed that in addition to the participation payment of £1, they had a 10 percent chance to earn up to £10 as an additional bonus, depending on their decisions during the study. We also informed them that their decisions would remain anonymous. Next, participants chose one out of three charities with which they preferred to be associated for the rest of the experiment. After that, participants were randomly assigned to one of four treatments (stage 1).

Stage 1 was a DG with the charity chosen by the participant. The type of DG and the information provided varied according to a 2 x 2 between-subjects design. The DG was either a standard DG or a DG with an opt-out option. In the DG with opt-out, participants could decide not to play the DG against a cost, which was 10 percent of the endowment (£1). Half of participants in both of these groups were randomly assigned to receive social information in the form of a descriptive norm (mean donation by participants in a previous session, including non-donors). The primary aims of stage 1 were to investigate (a) how many would "pay" to avoid playing the DG in the absence of social interactions and (b) to what extent doing so is influenced by social information.

In stage 2, all participants played a standard DG with the charity of their choice. This stage allowed us to capture how participants behave when they face a second donation request, depending on the options seen and the choices made in stage 1. Participants were only informed about the content of stage 2 after stage 1 to avoid strategic compensation behavior-i.e., participants reducing their donations in stage 1 because they knew that they could compensate by increasing it in stage 2 [START_REF] Gneezy | Conscience accounting: Emotion dynamics and social behavior[END_REF]. After the experiment, participants completed a survey about preferences and attitudes.1

This section also included an attention check to identify participants not paying attention.

In both stages, we included comprehension checks to ensure that participants understood the payment mechanism and the instructions of the games. Participants could not proceed to the following section unless they had answered the questions correctly. The initial endowment was £10 for each stage. Participants were told that only one of the two stages would be implemented (randomly chosen) for payment at the end of the experiment (as standard in the literature, see e.g., [START_REF] Brañas-Garza | Moral cleansing and moral licenses: Experimental evidence[END_REF]. This because "paying for all decisions makes wealth and portfolio effects possible, as well as cross-task contamination" (p. 142, [START_REF] Charness | Experimental methods: Pay one or pay all[END_REF]. Indeed, since we expect a treatment effect in stage 1, we would be unable to disentangle income effects from moral compensation effects in stage 2. We ensured incentive compatibility by paying a random subset of participants (1 out of 10). We explained the payment mechanism at the beginning of stage 1 and repeated it at the beginning of stage 2. As long as decisions are incentivized, random lottery payments produce results consistent with paying all [START_REF] Clot | Shall we pay all? An experimental test of Random Incentivized Systems[END_REF][START_REF] Umer | Effectiveness of random payment in Experiments: A meta-Analysis of dictator games[END_REF].

Before conducting the main study, we ran a pilot study on Prolific with 45 participants (not included in the main study) in order to collect data on mean donation for the social information and to test if instructions were clear. The pilot study included a standard DG and a DG with opt-out with a charity selected by the participant (from the same set as in the main study). In the standard DG, the mean donation was £5.5.

The main study had a total of 1400 participants.2 All participants lived in the UK and spoke English as first language. The mean completion time was 8.5 minutes. Participants received a fixed participation payment of £1 (for a payment of about 7 £/hour). Once data collection was completed, 10 percent of participants were randomly selected to receive the bonus payment according to their decision in either stage 1 or stage 2. We transferred them the amount corresponding to the payment bonus minus the stated donation, which was sent to the selected charity. 3Preregistration of the experimental design and hypotheses, along with the full experimental instructions, are available at this link. 4 Screenshots of the original experimental instructions are reported in Supplementary Material, Section 1.

Experimental design

Charity selection

Focusing on pro-environmental behavior as an instance of prosocial behavior, we asked participants to choose one from a set of three environmental charities, comprising WWF, Greenpeace, and Friends of the Earth. 5 We explained that they would be associated with the selected organization for the rest of the study without saying what decisions they would make in the later parts. Providing a few alternatives is common practice in this type of setting (e.g., [START_REF] Schmitz | Temporal dynamics of pro-social behavior: an experimental analysis[END_REF] because it reduces the probability that participants do not find an organization that they like while preventing choice overload [START_REF] Iyengar | When choice is demotivating: Can one desire too much of a good thing[END_REF]. We provided a short description of each charity based on information publicly available on the charity's website. We randomized the order of presentation of the charities.

Stage 1: Dictator game, opt-out option and social information

At this stage, participants were randomly assigned to one of four treatments with a 2×2 betweensubject design, where we varied the type of DG (standard or with opt-out) and the provision of social information.

In the standard DG (Standard) participants chose how to split an endowment of £10 between themselves and the environmental charity of their choice. In the DG with opt-out (Optout), participants could choose to pay £1 to skip the decision on how to split the endowment between themselves and the environmental charity. Opting out is inefficient and Pareto dominated by opting in, as the DG includes two allocations, (£9, £1) and (£10, £0), that dominate the opt-out allocation (£9, £0). We used a procedure similar to that of [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF] (and replicated by, e.g., [START_REF] Broberg | Is generosity involuntary?[END_REF][START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF] for the DG with opt-out, with two main differences.

First, in previous studies, another participant served as recipient, but remained uninformed about the DG in case the dictator opted out [START_REF] Broberg | Is generosity involuntary?[END_REF][START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF][START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF]. Here, to focus on self-image, we used a charity as beneficiary that would never know about dictators' decisions in any case. Second, [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF] introduced the opt-out option after participants played the DG, whereas we made participants decide whether to opt out before playing the DG (as in [START_REF] Lazear | Sorting in Experiments with Application to Social Preferences[END_REF]. Participants who chose to opt out did not see the screen with the DG and proceeded to the next part of the experiment. 6 This approach enables self-deception because opting out "hides" the donation request from participants. As a result, participants could overlook the donation request and maintain a positive self-image even if they did not donate. Additionally, if participants first made the donation decision and then encountered the opt-out option, their prior choice may have already boosted their self-image, influencing their subsequent decision to opt out [START_REF] Tonin | Experimental evidence of self-image concerns as motivation for giving[END_REF].

The social information was presented to half of participants playing either the standard DG (Standard-SN) or the DG with opt-out (Optout-SN). Social information was provided in the form of a descriptive norm. Specifically, participants were informed about the mean donations by participants who played the standard DG in the pilot study, considering also those allocating zero. Hence, as e.g., [START_REF] Allcott | Social norms and energy conservation[END_REF] and [START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF], we chose to use information about the mean behavior of the studied sample. Thus, no deception was involved. We used the following text: "For your information, we conducted earlier a similar survey on Prolific: participants gave on average £5.5 to the environmental organization". This information was provided to participants before the sharing decision in the Standard-SN treatment, and before the decision to opt out in the Optout-SN treatment.

In all treatments, participants chose how to split the endowment between themselves and the charity by selecting from a list of possible allocations. In order to force participants to either offer or keep more than the equal split, the equal split was not an option (as in [START_REF] Bellemare | Measuring inequity aversion in a heterogeneous population using experimental decisions and subjective probabilities[END_REF]. Available allocations thus started from (£0, £10) and incremented in steps £1 until reaching the allocation of (£4, £6). The next available allocations were (£4.5, £5.5) and (£5.5, £4.5). Allocations then continued to increment by £1, from (£6, £4) to (£10, £0). We randomized the order of presentation of the allocations in the list (ascending versus descending). Our randomization procedure assigned a higher proportion of participants to the treatments with the opt-out option, as follows: 30 percent to each of Optout and Optout-SN, and 20 percent to each of Standard and Standard-SN. Our sample size has 0.80 power to detect a fairly small effect size of social information and opt-out on donation (d = 0.24) and for the effect of social information on opt-out (d = 0.22), considering the threshold of statistical significance at 0.05.

Stage 2: Dictator game

All participants played a standard DG with the environmental charity of their choice. The endowment was £10. As in stage 1, the allocation decision was made out of a list of possible allocations that did not include the equal split. The order of presentation of the list was randomized and was kept consistent with the order used in stage 1 for each participant.

Behavioral predictions

In our setup, playing the DG is a dominant strategy. The costly opt-out option is Pareto dominated by allocations more favorable to the decision-maker (£10, £0) or to the recipient (£9, £1). However, there is empirical evidence that some individuals avoid prosocial requests to preserve their image while pursuing their self-interest. Indeed, the amount given to the recipient can signal the decision-maker's altruism, to the recipient when there is a defined one (social image), but also to the decision-maker herself (self-image). Therefore, individuals driven by image motivation may feel compelled to donate to signal that they are altruistic, although they would rather behave selfishly. Opting out represents a strategy to keep a large payoff and simultaneously preserve the social-and the self-image. In our setting, we only focus on self-image motivation because choices are anonymous and there is no participant recipient with expectations to meet [START_REF] Tonin | Experimental evidence of self-image concerns as motivation for giving[END_REF]. Opting out allows individuals to act as if the donation request did not exist and, thus, permits them to preserve their self-image even in the absence of a donation [START_REF] Adena | Online fundraising, self-image, and the long-term impact of ask avoidance[END_REF]. In our experiment, this selfdeception is facilitated by eliciting participants' decision to opt out before seeing the donation request.

We hypothesize that some participants donate to preserve their self-image. They are thus sensitive to the presence of the opt-out option and opt out as long as the expected benefits of doing so are higher than the costs. 7 Since we expect fewer donations when opt-out is possible, we should see a reduction in mean donations when the opt-out option is present, as hypothesized below.

Hypothesis 1. In stage 1, mean donation is higher in the Standard treatment than in the Optout treatment.

In the social information treatments, the descriptive norm is made salient and is expected to increase giving [START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF][START_REF] Krupka | The focusing and informational effects of norms on pro-social behavior[END_REF].8 Individuals tend to conform to peer behavior, to conditionally cooperate, or to use others' donations as a signal of charity quality. Thus, on average, we expect to replicate the commonly observed positive effect of social information on donations in the Standard treatment.

Hypothesis 2. In stage 1, in the standard DG, mean donation is higher when social information is displayed (Standard-SN) than when it is not displayed (Standard).

The effect of social information may also affect self-image motivation. Individuals may see others' behavior as the right thing to do. Thus, donating less than others may negatively affect the self-image, because one falls short of others' good behavior. The negative implications for the self-image of donating a low amount are, now that social information is salient, higher. Therefore, we expect that participants who would have given (i) because driven by self-image motivation and (ii) an amount below the descriptive norm, are more likely to opt out when social information is provided than when it is not provided, thus leading to an overall increase in opt-outs in the Optout-SN treatment.

Hypothesis 3. In the DG with opt-out, more participants opt out when social information is displayed (Optout-SN) than when it is not displayed (Optout).

Our last set of predictions refers to the behavior in the second DG. In stage 2, we examine how participants behave in a subsequent donation request depending on the options they saw in stage 1 and the choices they made. In order to eliminate the effect of accumulation of earnings, we only pay one randomly selected stage [START_REF] Charness | Experimental methods: Pay one or pay all[END_REF]. We also prevented strategic behavior by informing participants about the donation in stage 2 after having completed stage 1 [START_REF] Gneezy | Conscience accounting: Emotion dynamics and social behavior[END_REF]. Replicating a standard DG for all four treatments allows us to reveal the effect of self-image on subsequent prosocial behavior. Theoretically, rational decision-makers with prosocial preferences should behave consistently across the two stages, as only one decision is implemented. However, a first prosocial behavior tends to guarantee benefits to individuals, such as warm-glow and improved self-image, which may license them to reduce their donation in subsequent decisions (e.g., [START_REF] Brañas-Garza | Moral cleansing and moral licenses: Experimental evidence[END_REF][START_REF] Schmitz | Temporal dynamics of pro-social behavior: an experimental analysis[END_REF]. Thus, we expect an overall reduction in donation from stage 1 to stage 2 when the first game is a standard DG (Standard). We expect the same pattern among participants opting into the DG in the Optout treatment, as they may also have residual benefits from their donation in stage 1. Finally, we expect that participants opting out in stage 1 donate a positive amount in stage 2. This is because they cannot avoid the DG in stage 2, and thus donate a positive amount to self-signal that they are altruistic. The need for self-signaling their altruism is even more necessary because they did not establish a positive self-image in stage 1, since they avoided the donation request. Hypothesis 6. Those who opted out in stage 1 donate a positive amount in stage 2.

Empirical approach

To test whether mean donations across treatments differ, we perform pairwise comparisons by correcting for multiple hypothesis testing, following [START_REF] List | Multiple hypothesis testing in experimental economics[END_REF]. Unlike a two-by-two comparison of treatments (or a regression framework), this statistical technique adjusts for the familywise error rate and provides more reliable significance values comparing all treatments simultaneously. For Hypotheses 4 and 5, we compare mean donations for the same treatment between the two stages using paired t-tests. We test Hypothesis 6 through t-tests for mean donations equal to 0 for participants who opted out in stage 1. All our statistical tests have two-tailed alternative hypotheses. As a robustness check, we report the results of alternative model specifications in Supplementary Material, Section 5, which lead to the same conclusions as the analyses reported in the main text.

An overview of the descriptive statistics of the results is reported in Table 1. Distributions of donations in each stage and per treatment are reported in Figure 1 and Figure 2.

Behavior in stage 1

Results from our pairwise mean comparisons are reported in Table 2. In line with hypothesis 1, our results show that including an opt-out option reduces donations. The difference in mean donations between the Standard and Optout treatments is £0.93, which is almost 10 percent of the initial endowment and is statistically significant at p < 0.001. The reduction in mean donation can be attributed to the 9 percent of participants who opted out of the DG in the Optout treatment. The optout rate we find is lower than those observed in studies using a similar experimental design but with social interactions [START_REF] Broberg | Is generosity involuntary?[END_REF][START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF][START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF]. This suggests that the motivation to preserve a positive self-image is less compelling than the motivation to maintain a positive image in the eyes of others. We will return to this point in Section 6.

Interestingly, environmental identity is positively correlated with the decision to opt in and donate a positive amount and negatively correlated with the decision to opt in and not donate, and even more strongly, with the decision to opt out (see Table S4 in Supplementary Material). This indicates that participants driven by preferences over the charity's payoff donated, whereas those primarily concerned with their self-image but less concerned about the charity's payoff tended to avoid the donation request. it seems that the descriptive norm we communicated to participants (£5.5) was not high enough to incentivize them to donate, with the mean donation and the intensive margin in the control group being the same or above the descriptive norm (see Table 1).

Social information thus appears to affect participants' behavior negatively: it anchored participants' donations for those who donated a positive amount to £5.5 in the Standard-SN treatment (see Table 1). Moreover, it caused a shift in the distribution of donations, albeit not statistically significant. Fewer participants donated more than the descriptive norm in the Standard-SN treatment than in the Standard treatment (-5 percentage points), while more participants donated the same amount as the descriptive norm (+1.5 percentage points) or less (+3.5 percentage points). This asymmetric effect between participants who would have donated more or less than the norm is consistent with loss aversion [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF], as donating more than the others could be considered a "loss" and less a "gain". Thus, social information affected behavior, but, on average, it anchored donations to an amount lower than what would have been without this information.

Next, we find directional evidence that social information increases opt-outs. Ten percent of participants opted out when informed about the descriptive norm, compared to eight percent when this information was not reported. Although the difference goes in the direction stated in Hypothesis 3, it is not statistically significant (see Table 1). The difference is equivalent to 1.7 percentage points, which is rather small, and the effect size might have been too small to be detected with our sample size (type 2 error). However, despite the modest absolute difference in the number of opt-outs between the Optout and Optout-SN treatments, the relative increase of 20.7 percent in opting out is noteworthy. With a larger population, the impact of social information on avoiding a donation request could be substantial.

The suggestive positive effect of social information on opt-outs in the Optout-SN treatment may appear inconsistent with its negative effect on mean donation in the Standard-SN treatment. To reconcile these seemingly contrasting results, we shall consider that the social information has a different effect depending on how much participants would donate without it. Social information typically increases donations for those who would donate less than the descriptive norm, and it reduces donations for those who would donate more. Opting out may be more common among participants who would donate less than the social norm, because a relatively small donation may be enough to preserve the self-image. Thus, for these participants, the descriptive norm included in our social information may have exceeded the intended contribution if they were to opt in, making them more likely to opt out. This may reconcile why social information reduces donations in the Standard-SN treatment while (slightly) increases opt-outs in the Optout-SN treatment. Had we used a higher descriptive norm, social information may have increased donations in the Standard-SN treatment and opt-outs in the Optout-SN treatment significantly. Be that as it may, future research is needed to formally test our conjecture.

Difference between stage 1 and stage 2

Hypothesis 4 posits a reduction in donations in stage 2 among participants initially exposed to the standard DG. Accordingly, Table 3 shows that we can reject the null hypothesis that donations are equal across the two stages for the Standard treatment (p = 0.02). Next, we find directional evidence in support of hypothesis 5, with a non-statistically significant (p = 0.08) reduction in donations among participants who could, but did not, opt out in the Optout treatment. Interestingly, the acceptance of hypothesis 4, on the one hand, and the non-acceptance of hypothesis 5, on the other hand, show that there are different compensation behaviors when participants have to play the DG compared to when they decide to opt into it. In the Standard treatment, where opting out is not possible in stage 1, individuals driven by self-image motivation and those driven by preferences for the charity's payoff donated. Putting together the behavior of participants with these two types of motivation yields a significant reduction in donations from stage 1 to stage 2. In contrast, participants who opted into the DG in stage 1 in the Optout treatment and donated to the charity, did so because they have preferences over the charity's payoff; such preferences appear to make them behave consistently across the two stages. For them, what matters most is the charity's payoff, whereas warm-glow or improved self-image from giving in stage 1 is less relevant and does not lead to a significant reduction in donations in stage 2. Hence, the often observed decline in prosocial behavior following an initial prosocial act may primarily result from individuals driven by self-image motivation. After having established a positive self-image, they feel licensed to reduce their prosocial behavior.

Table 3 also shows that in both types of DG, donations do not significantly decline over time when social information is provided. Different explanations may account for this result. One explanation is that there may be little self-image benefits of donating to comply with others' behavior, and thus participants may feel that they still need to establish their self-image in stage 2. Alternatively, social information may have acted as an anchor, and participants stick to it in stage 2 too. This seems relevant for the Standard-SN treatment, as the intensive margin is close to the descriptive norm also in stage 2 in this treatment. In sum, our results suggest a positive effect of social information provided in a first decision on subsequent ones, but our design does not allow us to disentangle the different explanations underlying this result. We encourage further research on this topic, as only a handful of

studies have yet addressed it, with mixed findings [START_REF] Carlsson | Behavioral spillover effects from a social information campaign[END_REF][START_REF] Jessoe | Spillovers from Behavioral Interventions: Experimental Evidence from Water and Energy Use[END_REF][START_REF] Lasarov | The backfire effect of sustainable social cues. New evidence on social moral licensing[END_REF].

Finally, we confirm hypothesis 6, which focuses on participants opting out in stage 1, and posits that they donate a positive amount in stage 2. Accordingly, we find that 68.4 percent of participants who opted out in stage 1 donated a positive amount in stage 2, and the mean donation is statistically significantly higher than 0 in stage 2 for both the Optout and Optout-SN treatments (N = 32, mean = £2.34, SE = 0.42, p < 0.001 for Optout; N = 44, mean = £1.92, SE = 0.35, p < 0.001 for Optout-SN). As a comparison, participants who opted into the DG in the Optout and Optout-SN treatments, but gave nothing in stage 1, have a mean donation in stage 2 that is not significantly different from 0 (N = 43, mean = £0.25, SE = 0.23, p = 0.28).

Discussion and conclusions

The share of participants who used the costly opt-out option to avoid the donation request in our study is 9.2 percent. This share is lower compared to previous studies with similar settings but with a participant beneficiary [START_REF] Broberg | Is generosity involuntary?[END_REF][START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF][START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF][START_REF] Lazear | Sorting in Experiments with Application to Social Preferences[END_REF].

For example, with a payment scheme similar to ours, approximately 28 and 43 percent of the sample opted out of the DG in study 1 and study 2 (replication treatment) in [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF]. In these studies, it is assumed that the primary motivation behind opting out is the fear of making a donation that falls short of the recipient's expectations or that signals to others that one is not altruistic [START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF]. In contrast, in our study, the recipient is a charity, who would never know the source of the donation. Thus, opting out must be motivated by the desire to preserve one's self-image while behaving selfishly, by "overlooking" the donation request. A lower share of opt-outs in our study may thus imply that self-image motivation plays a lesser role than social image motivation as driver for prosocial behavior.

An alternative explanation for why we find a lower share of opt-outs than previous studies may be that individuals are more willing to share with charities than with another participant [START_REF] Umer | Unearned Endowment and Charity Recipient Lead to Higher Donations: A Meta-Analysis of the Dictator Game Lab Experiments[END_REF]. This explanation is supported by our finding that giving in our DG with a charity is on the higher end of the range found in previous DGs [START_REF] Engel | Dictator games: A meta study[END_REF]. Future research is needed to disentangle these two effects and isolate the driver underlying the smaller share of opt-outs when the recipient is a charity.

Next, we observe an unexpected negative effect of social information on donations when the DG could not be avoided. Our social information conveyed the descriptive norm, formulated from a different sample of the same population, including also non-donors (as, for example, [START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF]. Expost, the social information amount we chose may not have been high enough to increase donations, as it was too close to the average, "common" behavior in the control group. Information about the high prevalence of the prosocial behavior might have been more effective [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF][START_REF] Shang | A Field Experiment in Charitable Contribution: The Impact of Social Information on the Voluntary Provision of Public Goods[END_REF]. However, high descriptive norms are not always easy to report because they might require manipulating the reference sample used as basis to create the norm (e.g., [START_REF] Bicchieri | Do the right thing: But only if others do so[END_REF] or manipulating the norm itself (e.g., [START_REF] Agerström | Using descriptive social norms to increase charitable giving: The power of local norms[END_REF]. Alternatively, they might communicate the contribution of a single, high-performing participant (e.g., [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF][START_REF] Shang | A Field Experiment in Charitable Contribution: The Impact of Social Information on the Voluntary Provision of Public Goods[END_REF], possibly creating suspicion about how the participant was selected. If using random draws from the population, it may be more effective to inform about the extensive margin (as in [START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF][START_REF] Frey | Social Comparisons and Pro-social Behavior: Testing "Conditional Cooperation" in a Field Experiment[END_REF][START_REF] Krupka | The focusing and informational effects of norms on pro-social behavior[END_REF][START_REF] Krupka | The focusing and informational effects of norms on pro-social behavior[END_REF], than the intensive margin (as we did). Future research should systematically investigate this aspect to better understand the impact of different frames of social information on prosocial behavior.

Although social information reduced donations in the standard DG, we find directional evidence that it increased the choice to avoid the DG. In line with our result, D'Adda et al. ( 2018) find a nonsignificant effect of social pressure alone on demand for information about the emissions caused by air conditioning. Yet, they find that when social pressure is combined with other treatments that generate a feeling of moral obligation to act pro-environmentally, it causes significant information avoidance. Similarly, [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF] shows that the effect of social information on avoidance of a donation request depends on the level of the descriptive norm. Collectively, these results suggest that social norms (in their different forms) can lead to avoidance of a prosocial request, but only when they are high enough. Since our social information was relatively low, it may have caused a few optouts, possibly insufficient to detect a statistically significant effect. Hence, an extension of our study with a higher descriptive norm is needed to provide robust evidence for the interplay between selfimage motivation and social information. Moreover, it is worth exploring the mechanism underlying the interaction between self-image motivation and social information: does social information have negative (as proposed by us) or positive (as proposed by [START_REF] Klinowski | Reluctant donors and their reactions to social information[END_REF]) implications for the selfimage that leads to avoidance of the donation request?

Finally, we offer a self-image perspective to elucidate temporal dynamics in prosocial behavior.

Notably, the behavior in the second stage appears to hinge on the motivation to give. When preferences over the charity's payoff drive giving, participants tend to exhibit consistent behavior over time. Instead, when self-image motivation drives donation, participants tend to reduce the amount given in the second donation. Note: envID is measured as unweighted mean response to the following items [START_REF] Panzone | The impact of environmental recall and carbon taxation on the carbon footprint of supermarket shopping[END_REF]: "Being environmentally responsible is an important part of who I am"; "I view myself as an environmentally responsible person"; "Being environmentally responsible is not really important to me" (R); "I strongly aspire to be environmentally responsible". donating frequency and volunteering frequency represent how often participants donate money and volunteer for environmental organizations, respectively [START_REF] Zhang | Consumer environmental engagement and the intention to adopt emerging sustainable transport options in China and Denmark[END_REF]. Support for each environmental charity is measured as unweighted mean response to the following items: "I am familiar with the association"; "I trust the association"; "I support their actions". All responses are given on 5-point Likert scale. 1 P-value from ANOVA.

3 Changes compared to the pre-registration and test of pre-registered hypotheses

We pre-registered six hypotheses. In the manuscript, Hypotheses 2, 3 and 6 remain unchanged, while we made minor changes to Hypotheses 1, 4 and 5, as explained in Table S2. The revised hypotheses refer to the effect of the opt-out option in the absence of social information. Indeed, we anticipated that social information would affect why and how much people donate. Failing to distinguish for the presence of social information may thus confound the results. Testing the original set of hypotheses (reported in Table S3) yields virtually the same conclusions as the revised hypothesis testing discussed in the main text. The only difference is that in the original formulation, we accept hypothesis 5 with p = 0.05, whereas in the updated formulation we fail to reject the null hypothesis being the p-value above the threshold of statistical significance (p = 0.08). The original formulation posited a reduction in donations among participants opting into the DG considering both the Optout and Optout-SN treatments, while the updated formulation only focuses on the Optout treatment. In any case, the reduction in donations among participants forced to play the DG in the Standard treatment is more than twice than that of participants deciding to play the DG in the Optout treatment, suggesting that temporal dynamics depend on the motivation to donate in the first decision.

Relation between participants' characteristics and donor profile

Hypothesis 4 .

 4 Mean donation is lower in stage 2 than in stage 1 in the Standard treatment. Hypothesis 5. Mean donation among participants opting in is lower in stage 2 than in stage 1 in the Optout treatment.

Figure

  Figure 1. Distribution of donations in stage 1 per treatment

1

  Screenshots of the original experimental instructionsCharity selection [common to all treatments] Decision screen for opt out [treatment Optout-SN] Decision screen for donation, stage 1 [treatments Standard, Optout, Optout-SN; in Optout and Optout-SN only participants answering yes to the preceding question see this screen]2 Descriptive statistics and survey items

Table 1 . Mean donations in stage 1 and stage 2, and number of opt-outs, per treatment

 1 : extensive margin represents the share of participants donating a positive amount (for stage 1 this variable is 0 also for opt-outs); intensive margin represents the amount donated conditional on donating a positive amount. Standard deviations in parentheses. 1 P-value from ANOVA. * p < 0.05, ** p <0.01, *** p < 0.001.

	Treatment	Standard Standard-SN Optout Optout-SN P-value 1
	N	291	280	388	441
	Stage 1
	Mean donation	5.48	4.89	4.55	4.22	< 0.001***
		(2.82)	(2.81)	(3.09) (2.85)
	Share of opt-out	-	-	0.082 0.100	0.39
				(0.27) (0.30)
	Extensive margin 0.92	0.89	0.87	0.85	0.01*
		(0.26)	(0.31)	(0.34) (0.36)
	Intensive margin 5.93	5.48	5.25	4.98	< 0.001***
		(2.44)	(2.37)	(2.71) (2.40)
	Stage 2
	Mean donation	5.29	4.83	4.66	4.37	< 0.001***
		(2.89)	(2.92)	(2.96) (2.74)
	Extensive margin 0.91	0.89	0.92	0.90	0.47
		(0.28)	(0.32)	(0.27) (0.30)
	Intensive margin 5.78	5.45	5.07	4.84	< 0.001***
		(2.50)	(2.50)	(2.73) (2.45)

Note

Table 2 . Pairwise comparisons of mean donations in stage 1

 2

	Mean donations comparison	Difference in means	P-value 1
	Standard vs Standard-SN	0.587	0.030*
	Standard vs Optout	0.933	< 0.001***
	Standard vs Optout-SN	1.254	< 0.001***
	Standard-SN vs Optout	0.346	0.127
	Standard-SN vs Optout-SN	0.667	0.004**
	Optout vs Optout-SN	0.322	0.205
	Note: 1 P-values from pairwise mean comparison corrected with Theorem 3.1 in List et al. (2019). * p < 0.05,
	** p <0.01, *** p < 0.001.
	However, we do not find any evidence for social information to increase mean donations (in contrast
	to hypothesis 2). Instead, social information reduced mean donation by £0.59, which is significant at
	p = 0.03. This is due to a lower intensive margin in the Standard-SN treatment than in the Standard

treatment (p = 0.034), while there is no significant effect on the extensive margin (p = 0.19). Ex-post,

Table 3 . Test on equality of mean donations between stage 1 and stage 2, per treatment

 3

	Treatment	Difference in means, stage 2-stage 1 P-value 1
	Standard	-0.192	0.021*
	Standard-SN -0.064	0.435
	Optout a	-0.084	0.080
	Optout-SN a -0.053	0.279

Note: a Participants opting out are excluded. 1 P-value from two-tailed paired t-test. * p < .05, ** p < .01, *** p < .001.

Table S4 . Descriptive statistics per treatment

 S4

		Standard Standard-SN Optout Optout-SN P-value 1
	N	291	280	388	441
	female	0.62	0.55	0.57	0.65	0.03
	age (years)	38.8	39.6	39.8	39.8	0.73
		(13)	(12.8)	(13)	(13)
	graduate degree	0.57	0.58	0.57	0.57	0.98
	income (k€)	22.7	23.8	23	23	0.85
		(16.4)	(15.4)	(14.8) (15.7)
	student	0.13	0.1	0.14	0.13	0.52
	envID	3.66	3.64	3.67	3.65	0.95
		(0.89)	(0.87)	(0.81) (0.80)
	donating frequency	2.51	2.6	2.6	2.51	0.58
		(1.19)	(1.19)	(1.18) (1.16)
	volunteering frequency 2.32	2.31	2.17	2.28	0.45
		(1.39)	(1.39)	(1.36) (1.36)
	support WWF	4.18	4.23	4.21	4.18	0.71
		(0.73)	(0.69)	(0.69) (0.68)
	support FriendsEarth	3.28	3.37	3.40	3.38	0.44
		(0.94)	(0.93)	(0.96) (0.90)
	support Greenpeace	3.54	3.57	3.64	3.59	0.42
		(0.81)	(0.84)	(0.80) (0.81)
	Charity selection
	WWF	0.63	0.65	0.63	0.65	0.87
	Friends of the Earth	0.21	0.20	0.20	0.22	0.88
	Greenpeace	0.16	0.15	0.18	0.13	0.35

Table S5 . Original and updated hypotheses

 S5 Standard&Standard-SN refers to aggregating treatments Standard and Standard-SN. Optout&Optout-SN refers to aggregating treatments Optout and Optout-SN.

	HP Original			Updated	Explanation
	1	In stage 1, mean donation is	In stage 1, mean	By isolating the impact of the opt-out option
		higher	in	treatments	donation is higher in	and excluding the influence of social
		Standard&Standard-SN than	the	Standard	information on the decision to opt-out, we
		in		treatments	treatment than in the	examine the propensity to avoid a donation
		Optout&Optout-SN.	Optout treatment.	request in a standard DG with a charity.
	4	Mean donation is lower in	Mean donation is	We anticipate that social information affects
		stage 2 than stage 1 in	lower in stage 2 than	decisions in stage 1, thereby potentially
		treatments			in stage 1 in the	influencing also behavior in stage 2. We thus
		Standard&Standard-SN.	Standard treatment.	examine the behavior of participants in stage 2
	5	The amount donated among	Mean	donation	when no additional stimuli are provided,
		agents opting in is lower in	among participants	differentiating for whether participants have
		stage 2 than stage 1 for	opting in is lower in	to play the DG (Hypothesis 4) or decide to opt
		treatments Optout&Optout-	stage 2 than in stage	into it (Hypotheses 5).
		SN.			1 in the Optout
					treatment.

Note:

Table S6 . Test of the hypotheses included in the pre-registration

 S6 Standard&Standard-SN refers to aggregating treatments Standard and Standard-SN. Optout&Optout-SN refers to aggregating treatments Optout and Optout-SN. * p < 0.05, ** p < 0.01, *** p < 0.001.

	HP Test	P-value	Interpretation
	1	Two-sided t-test for equality in mean donations between	<0.001*** The presence of the opt-out
		conditions without (Standard&Standard-SN) and with		option reduces donations
		opt-out (Optout&Optout-SN), stage 1
	4	Two-sided paired t-test for equality in mean donations	0.03*	Mean donations reduce in stage
		between stage 1 and stage 2 for conditions without the		2 when opt out is not possible
		opt-out option (Standard&Standard-SN)		in stage 1
	5	Two-sided paired t-test for equality in mean donations	0.05*	Mean donations reduce in stage
		between stage 1 and stage 2 among those who opt into		2 among those who opt into the
		the DG in stage 1 (Optout&Optout-SN)		DG in stage 1
	Note:

Table S7 . Multinomial probit results for the relation between characteristics and decisions in stage 1 in treatment Optout (marginal effects)

 S7

	5 Robustness tests
	5.1
		(1)			(2)
		Donors Non-donors Avoiders Donors Non-donors Avoiders
	envID	0.050 *** -0.019 *	-0.032 *** 0.042 *** -0.014	-0.028 *
		(0.015) (0.009)	(0.012)	(0.016) (0.009)	(0.013)
	female	0.073 *** -0.048 ***	-0.026	0.073 *** -0.048 ***	-0.025
		(0.026) (0.017)	(0.021)	(0.026) (0.017)	(0.021)
	age	0.001	-0.001	0.001	0.001	-0.001	0.001
		(0.001) (0.001)	(0.001)	(0.001) (0.001)	(0.001)
	income	0.001	0.001	0.001	0.001	0.001	0.001
		(0.001) (0.001)	(0.001)	(0.001) (0.001)	(0.001)
	graduate	0.022	0.009	-0.031	0.024	0.009	-0.033
		(0.026) (0.015)	(0.021)	(0.026) (0.015)	(0.022)
	volunteering frequency				0.002	-0.001	0.001
					(0.01)	(0.006)	(0.008)
	donating frequency				0.025 *	-0.012	-0.013
					(0.011) (0.006)	(0.009)
	student				0.03	-0.004	-0.026
					(0.035) (0.021)	(0.028)
	N	826			814
	Note: Donors are participants who opt in and donate a positive amount; Non-donors are participants who
	opt in and do not donate; Avoiders are participants who opt out. Robust standard errors in parentheses. *
	p < 0.05, ** p < 0.01, *** p < 0.001.
			34

Interactions between treatments and gender Table S8. OLS regression results on treatment effects on donations in stage 1 (Column 1), including interactions between treatments and gender (Column 2); on probability to opt out (Column 3), including interactions between treatments and gender (Column 4); on donations in stage 2 (Column 5), including interactions between treatments and gender (Column 6)

  Standard in Columns 1 and 2; Optout in Columns 3 and 4. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

	5.2
		(1)	(2)	(3)	(4)	(5)	(6)
	Standard-SN	-0.510 *	-0.442			-0.381	-0.432
		(0.223) (0.354)			(0.227) (0.354)
	Optout	-0.919 *** -0.786 *			-0.611 *** -0.591
		(0.217) (0.336)			(0.214) (0.326)
	Optout-SN	-1.305 *** -1.215 *** 0.019	0.015	-0.969 *** -0.861 ***
		(0.204) (0.329) (0.020) (0.035) (0.205) (0.327)
	envID	0.860 *** 0.859 *** -0.032 * -0.032 * 0.988 *** 1.027 ***
		(0.094) (0.094) (0.014) (0.014) (0.152) (0.331)
	female	0.963 *** 1.092 *** -0.027	-0.031	0.885 *** 0.885 ***
		(0.155) (0.327) (0.022) (0.030) (0.094) (0.094)
	age	0.018 *** 0.018 *** -0.000	-0.000	0.021 *** 0.021 ***
		(0.006) (0.006) (0.001) (0.001) (0.006) (0.006)
	income	0.010	0.010	-0.000	-0.000	0.011 *	0.011 *
		(0.005) (0.005) (0.001) (0.001) (0.005) (0.005)
	graduate	-0.267	-0.270	-0.031	-0.031	-0.348 *	-0.349 *
		(0.156) (0.156) (0.021) (0.021) (0.152) (0.152)
	Standard-SN x female		-0.107				0.097
			(0.455)				(0.461)
	Optout x female		-0.221				-0.033
			(0.442)				(0.432)
	Optout-SN x female		-0.143		0.007		-0.169
			(0.420)		(0.042)		(0.420)
	constant	0.950 *	0.867	0.245 *** 0.246 *** 0.560	0.542
		(0.431) (0.460) (0.060) (0.060) (0.431) (0.456)
	p-value of Optout = Optout-SN 0.05
	R 2	0.126	0.126	0.016	0.016	0.128	0.128
	N	1395	1395	826	826	1395	1395
	Note: baseline treatment: 35

Alternative model specifications Table S9. Hurdle model results on treatment effects on donations in stage 1 and stage 2 (marginal effects)

  Avg represents both steps of the hurdle model. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

		Donations stage 1	Donations stage 2
		E	I	Avg	E	I	Avg
	Standard-DN -0.025	-0.410	-0.509 *	-0.019	-0.305	-0.378
		(0.023) (0.212) (0.230)	(0.024) (0.218) (0.234)
	Optout	-0.057 *	-0.675 *** -0.909 *** 0.008	-0.697 *** -0.603 ***
		(0.023) (0.196) (0.214)	(0.021) (0.199) (0.212)
	Optout-DN	-0.084 *** -0.965 *** -1.288 *** -0.019	-0.941 *** -0.950 ***
		(0.023) (0.191) (0.207)	(0.022) (0.194) (0.207)
	envID	0.049 *** 0.721 *** 0.882 *** 0.043 *** 0.763 *** 0.901 ***
		(0.010) (0.086) (0.089)	(0.009) (0.087) (0.088)
	female	0.073 *** 0.669 *** 0.955 *** 0.069 *** 0.711 *** 0.983 ***
		(0.018) (0.145) (0.154)	(0.016) (0.146) (0.151)
	age	0.001	0.014 *** 0.018 *** 0.001 *	0.016 *** 0.021 ***
		(0.001) (0.005) (0.006)	(0.001) (0.005) (0.006)
	income	0.001	0.008	0.010 *	0.001	0.009	0.011 *
		(0.001) (0.005) (0.005)	(0.001) (0.005) (0.005)
	graduate	0.004	-0.331 *	-0.274	-0.015	-0.297 *	-0.346 *
		(0.018) (0.142) (0.155)	(0.016) (0.143) (0.152)
	N		1395			1395

Note: E represents extensive margin; I represents intensive margin,

Table S10 . Differences-in-differences results for treatment effect and temporal dynamics

 S10 : participants opting out are excluded. The dependent variable is donation at each stage. Baseline treatment: Standard. Clustered robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001. Emmanuelle Lavaine « The Heterogeneous Effects of Lockdown Policies on Air Pollution » WP 2023-06 Valeria Fanghella, Lisette Ibanez & John Thøgersen « To request or not to request: charitable giving, social information, and spillover »

		CEE-M Working Papers 1 -2023
			(1)
	WP 2023-01	Standard-SN Optout Pauline Castaing & Antoine Leblois « Taking firms' margin targets seriously in a model of competition in supply -0.511 * (0.223) -0.536 * (0.215) functions »
		Optout-SN	-0.866 ***
	WP 2023-02	(0.201) Sylvain Chabé-Ferret, Philippe Le Coënt, Caroline Lefébvre, Raphaële stage 2 -0.193 * (0.083) Standard-SN x stage 2 0.129 (0.117) Préget, François Salanié, Julie Subervie & Sophie Thoyer « When Nudges Backfire: Evidence from a Randomized Field Experiment to Boost Biological Pest Control »
		Optout x stage 2	0.109
	WP 2023-03	(0.096) 0.141 Adrien Coiffard, Raphaële Préget & Mabal Tidball Optout-SN x stage 2 « Target versus budget reverse auctions: an online experiment using the (0.097) envID 0.852 *** strategy method »
	WP 2023-04	(0.093) 0.956 *** (0.151) 0.021 *** (0.006) Simon Mathex, Lisette Hafkamp Ibanez & Raphaële Préget female age « Distinguishing economic and moral compensation in the rebound effect: A theoretical and experimental approach »
	WP 2023-05	income Simon Briole, Augustin Colette &	0.010 + (0.005)
		graduate	-0.371 *
			(0.149)
		constant	0.949 *
			(0.423)
		p-value Standard-SN x stage 2 + stage 2 = 0 0.435
		p-value Optout x stage 2 + stage 2 = 0	0.080
		p-value Optout-SN x stage 2 + stage 2 = 0	0.291
		R 2	0.121
		N	2638
		# clusters	1319

Note

More details about survey items and descriptive statistics are available in Supplementary Material, Section

In the same section, we also report participants' characteristics by treatment. TableS1shows that the randomization was pretty successful, except for gender, which is slightly unbalanced across treatments. We rule out that this unbalance drives our results in Supplementary Material, Section 5.

Out of the 1442 participants who started the main study, 1404 participants completed it. We rejected 4 participants; two of them because they took less than 5 minutes to complete the experiment and failed the attention check; one completed the survey in less than one minute with the wrong completion code; and one used a Prolific ID that was not associated to any identifier in the Prolific database. At the beginning of the data collection, a few participants saw a table in which the payoffs for the charity and the participant were interchanged. To address this issue, we reached out to the 14 participants who might have been affected by this issue and asked them to verify their allocations. Our results remain unchanged whether we include or exclude them in the analyses (results are available upon request).

Overall, 146 participants received a bonus, for a total of £798.5, and we donated £460, £78 and £123.5, to WWF, Greenpeace, and Friend of the Earth, respectively. We used the same incentive mechanism also for the pilot study. Of the 146 participants receiving a bonus,

were drawn from the sample of the pilot study and 142 from the main study.4 We made some minor changes to the hypotheses formulation after having received peer feedback. The new hypotheses better fit the collected data and respond to our research questions. We report these changes in Supplementary Material, Section 3. In the same section we also report testing of the original hypotheses and show that they lead to the same conclusions as the updated formulations.

These organizations are quite popular in the UK and are seen as efficient in their resource use (https://www.theguardian.com/environment/2013/nov/27/1-in-10-uk-adults-environmental-group, last accessed on 10/01/2022).

A possible alternative reason for opting out is to reduce the time required to complete the survey. However, we asked participants whether they wanted to opt out just before the donation decision, making the difference in completion time between those who opt out or not negligible (p = 0.93 from ANOVA).

Note that by fixing the cost to opt out at £1, we are not able to detect participants donating for self-image motivation with willingness to pay lower than £1. The decision to fix the price in this way is primarily to compare our results with those from[START_REF] Dana | What you don't know won't hurt me: Costly (but quiet) exit in dictator games[END_REF] and replications, and secondly, to ensure comprehension, as a multiple price list mechanism like the one by[START_REF] Broberg | Is generosity involuntary?[END_REF] may be difficult to implement in the online environment, which allows for less control over participants' behavior than the laboratory.

Except for pure altruists, who see others' and personal donations as substitutes. Thus, their marginal utility from donating reduces with the information that others donate more. In our experiment, we give only one value of descriptive norm; thus, we may expect it crowds out (in) for those who thought that the social norm of giving was lower (higher) than the descriptive norm.

CEE-M Working Papers / Contact : laurent.garnier@inrae.fr  RePEc https://ideas.repec.org/s/hal/wpceem.html  HAL https://halshs.archives-ouvertes.fr/CEE-M-WP/


Recent highly pathogenic avian influenza A(H5N1) outbreaks in two Korean cat shelters highlight the need to enhance surveillance for cross-species viral transmission into animal populations kept by humans for nonagricultural or non-conventional livestock farming purposes from a One Health perspective.

Cross-species viral transmission refers to the infection of a new host species by a virus, commonly referred to as 'spillover' [START_REF] Plowright | Pathways to zoonotic spillover[END_REF][START_REF] Parrish | Cross-species virus transmission and the emergence of new epidemic diseases[END_REF] . The current COVID-19 pandemic has clearly illustrated how cross-species viral transmission can negatively impact both human and animal health, with the potential to trigger future pandemics, thereby highlighting the importance of having effective and efficient surveillance for crossspecies viral transmission in place. Nonetheless, the challenge always remains in identifying the interfaces for cross-species viral transmission and distributing surveillance efforts optimally amongst these interfaces.

The research and public attention on cross-species viral transmission has primarily focused on enhancing our knowledge about a pool of potential zoonotic viruses in wildlife, monitoring the prevalence of known zoonotic viruses within wildlife or livestock, and assessing the risk of their transmission to humans, along with syndromic surveillance targeted at unexplained clinical cases in livestock and humans. Above all, these surveillance activities are concentrated at the interfaces where the economic and health impacts of cross-species transmission are considered significant [START_REF] Plowright | Pathways to zoonotic spillover[END_REF][START_REF] Li | Bats are natural reservoirs of SARS-like coronaviruses[END_REF][START_REF] Letko | Bat-borne virus diversity, spillover and emergence[END_REF] . However, surveillance in animal populations raised for non-conventional production purposes (e.g. minks and foxes for fur production) and those in non-agricultural settings (e.g. animal shelters, zoos, and places where visitors can touch companion, or wild animals) remains scarce globally, despite increasing attention to surveillance on mink and fox farms 5 in the context of recent SARS-CoV-2 and highly pathogenic avian influenza (HPAI) A(H5N1) outbreaks in these settings [START_REF] Agüero | Highly pathogenic avian influenza A(H5N1) virus infection in farmed minks, Spain, October 2022[END_REF][START_REF] Lindh | Highly pathogenic avian influenza A(H5N1) virus infection on multiple fur farms in the South and Central Ostrobothnia regions of Finland, July 2023[END_REF][START_REF] Oreshkova | SARS-CoV-2 infection in farmed minks, the Netherlands, April and May 2020[END_REF][START_REF] Peacock | Mink farming poses risks for future viral pandemics[END_REF] .

On July 25 th and 31 st , 2023, highly pathogenic avian influenza A(H5N1) infection, which has the potential to cause fatal disease in humans [START_REF]Human Infection with Avian Influenza A(H5) Viruses[END_REF] , was confirmed in two cat shelters in Seoul, South Korea [START_REF] Mafra | 5MiUyRjU2NjkwMyUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJT NEJTI2YmJzT3BlbldyZFNlcSUzRCUyNnBhZ2UlM0Q1JTI2cm93JTNEMTAlMjZwYXNzd29yZ CUzRCUyNnJnc0JnbmRlU3RyJTNEJTI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJ TI2aXNWaWV3TWluZSUzRGZhbHNlJTI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF][START_REF] Mafra | 5MiUyRjU2Njk0 OSUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJTI2YmJzT3BlbldyZFNlcSUzR CUyNnBhc3N3b3JkJTNEJTI2cGFnZSUzRDIlMjZyZ3NCZ25kZVN0ciUzRCUyNnJvdyUzRDEwJ TI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXNWaWV3TWluZSUzRGZhbHNlJ TI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF][START_REF]Exclusive] Mass Deaths of 38 Cats… Cause Identified as 'Avian Influenza[END_REF] . Briefly, at the cat shelter where the infection was first confirmed (Shelter 1), 38 out of the 40 cats died within a month, with the time between two consecutive deaths being ≤2 days [START_REF]Exclusive] Mass Deaths of 38 Cats… Cause Identified as 'Avian Influenza[END_REF] . This surge in deaths prompted the owner of Shelter 1 and its veterinarian to suspect a cause other than common respiratory infections in cats. Samples from two of the cats that had died from suspected respiratory infections were sent to a private diagnostic laboratory and confirmed to contain HPAI A(H5N1) virus by the Laboratory of Virology at the College of Veterinary Medicine, Seoul National University [START_REF]Exclusive] Mass Deaths of 38 Cats… Cause Identified as 'Avian Influenza[END_REF] . Then, the infection was confirmed again by the Animal and Plant Quarantine Agency (APQA) [START_REF] Mafra | 5MiUyRjU2NjkwMyUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJT NEJTI2YmJzT3BlbldyZFNlcSUzRCUyNnBhZ2UlM0Q1JTI2cm93JTNEMTAlMjZwYXNzd29yZ CUzRCUyNnJnc0JnbmRlU3RyJTNEJTI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJ TI2aXNWaWV3TWluZSUzRGZhbHNlJTI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF] after it was formally reported to the agency according to the Act on the Prevention of Animal Contagious Diseases: the Act mandates reporting animals, including cats, that have died of unidentified diseases or are suspected or confirmed to have been infected by contagious animal diseases types I, II, and III as defined by the Act [START_REF]Act on the Prevention of Animal Contagious Diseases[END_REF] . Several days later, a veterinarian reported respiratory symptoms in a cat from another shelter in Seoul (Shelter 2), and HPAI A(H5N1) infection was subsequently confirmed by the APQA [START_REF] Mafra | 5MiUyRjU2Njk0 OSUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJTI2YmJzT3BlbldyZFNlcSUzR CUyNnBhc3N3b3JkJTNEJTI2cGFnZSUzRDIlMjZyZ3NCZ25kZVN0ciUzRCUyNnJvdyUzRDEwJ TI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXNWaWV3TWluZSUzRGZhbHNlJ TI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF] . As of October 2023, influenza A(H5N1) infection has been confirmed in five cats from Shelter 1 and four cats from Shelter 2, all of which were reported to have died [START_REF] Mafra | 5MiUyRjU2NzI1OCUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJ TI2YmJzT3BlbldyZFNlcSUzRCUyNnBhZ2UlM0QxJTI2cm93JTNEMTAlMjZwYXNzd29yZCUzR CUyNnJnc0JnbmRlU3RyJTNEJTI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXN WaWV3TWluZSUzRGZhbHNlJTI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF][START_REF]World Animal Health Information System (WAHIS)[END_REF] . The information on the number of cats with negative test results has not been released yet.

Avian influenza surveillance in South Korea is primarily focused on the detection of infections on poultry farms and in wild birds. Surveillance in mammals started early this year. However, it only focused on specific wild mammalian species and did not include domestic cats [START_REF]Proactive Avian Influenza Surveillance in Wild Mammals[END_REF] . Not surprisingly, the detection of the virus in cats in both these cat shelters within a short timespan attracted widespread attention. A subsequent epidemiological investigation by the Ministry of Agriculture, Food and Rural Affairs (MAFRA) detected influenza A(H5N1) virus in cat food collected in Shelter 2, which contained duck meat, but not in cat food containing chicken meat. The MAFRA investigation concluded that raw duck and chicken meat had not been properly processed by the company that produced the cat food found to be contaminated [START_REF] Mafra | 5MiUyRjU2NzI1OCUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJ TI2YmJzT3BlbldyZFNlcSUzRCUyNnBhZ2UlM0QxJTI2cm93JTNEMTAlMjZwYXNzd29yZCUzR CUyNnJnc0JnbmRlU3RyJTNEJTI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXN WaWV3TWluZSUzRGZhbHNlJTI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF][START_REF] Mafra | JTJGYmJzJTJGaG9tZSUyRjc5MiUyRjU2Njk1NyUyRm FydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJTI2YmJzT3BlbldyZFNlcSUzRCUyNnBh Z2UlM0Q3JTI2cm93JTNEMTAlMjZwYXNzd29yZCUzRCUyNnJnc0JnbmRlU3RyJTNEJ TI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXNWaWV3TWluZSUzRGZhbHNlJ TI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF] . In a swift response, the MAFRA ordered the recall of all cat food production batches containing duck or chicken meat that were deemed at risk. Approximately 13,200 units of the two recalled products had already been sold to 286 customers, but no signs of infection have been reported amongst their cats which were monitored twice at a 14-day interval [START_REF] Mafra | 5MiUyRjU2NzI1OCUyRmFydGNsVmlldy5kbyUzRnJnc0VuZGRlU3RyJTNEJ TI2YmJzT3BlbldyZFNlcSUzRCUyNnBhZ2UlM0QxJTI2cm93JTNEMTAlMjZwYXNzd29yZCUzR CUyNnJnc0JnbmRlU3RyJTNEJTI2YmJzQ2xTZXElM0QlMjZzcmNoQ29sdW1uJTNEJTI2aXN WaWV3TWluZSUzRGZhbHNlJTI2c3JjaFdyZCUzRCUyNg%3D%3D[END_REF] . Considering also that all cats in the two shelters were known to have stayed indoors and HPAI infection had been confirmed on the country's poultry farms including duck farms until April 2023 [START_REF]World Animal Health Information System (WAHIS)[END_REF] , it is plausible that influenza A(H5N1) viral incursion originated from contaminated duck meat contained in cat food, particularly in Shelter 2. However, as of this writing, no definitive epidemiological or genomic evidence has been released by the MAFRA, and therefore, it is unknown whether cats in Shelter 1 were fed the same or similar products and whether cat-to-cat transmission occurred following initial exposure in the two shelters and, if it did, what its relative contribution was compared to potential food-to-cat transmission.

nature communications

(2023) 14:6958 | 1
So far, the management of the influenza A(H5N1) outbreaks in the cat shelters can be considered an example of good practice of surveillance and epidemiological investigations related to cross-species viral transmission. It has successfully detected influenza A(H5N1) infection in cats, identified a potential source of infection in at least one of the two shelters, and resulted in prompt transmission control measures. However, the question arises whether the MAFRA and APQA would be able to respond as successfully to cross-species viral transmission occurring in other epidemiological contexts. It has to be emphasised that the detection of influenza A(H5N1) outbreaks in the two cat shelters was initiated by the sudden deaths of multiple cats in Shelter 1 noticed by its owner and veterinarian. Subsequent steps taken by the veterinarians and virologists then led to the notification of the authorities, thereby initiating more detailed epidemiological investigations. This underscores the potential challenge of detecting crossspecies influenza A(H5N1) infection and identifying a potential source of contagion if contaminated cat food was solely distributed to privately-owned cats rather than shelter cats, or if any element of the aforementioned chain of events was absent. There are several possible reasons for this:

Firstly, under a given level of viral pressure, stochastic viral extinction may be more likely to occur when only a few cats in individual households are exposed to the virus as opposed to a larger group of cats. This is due to the increased contact rates between cats in a shelter as well as the increased likelihood of the virus successfully adapting to cats and subsequently transmitting between them, especially considering immunological barriers within individual cats 1 , although it is currently unknown whether any cat-to-cat transmission had occurred in the two shelters.

Secondly, the presence of infection of cats in different households would be more likely to be missed by animal health authorities. This is due to the challenge that veterinarians would face in suspecting influenza A(H5N1) infection when individual cats are presented to different veterinary clinics. Although HPAI infection in cats is notifiable, it is much less common than other respiratory infections in cats [START_REF] Binns | A study of feline upper respiratory tract disease with reference to prevalence and risk factors for infection with feline calicivirus and feline herpesvirus[END_REF] and is difficult to distinguish during the early infection stages. The fact that the reporting from Shelter 1 was made only after a substantial number of cats had died further emphasises the challenge veterinarians would face with limited prior experiences and knowledge about the risk and clinical manifestation of HPAI infection in cats. The recent identification of influenza A(H5N1) infections in privately-owned cats in Poland demonstrates that detecting the infection in such a scenario is not entirely implausible [START_REF] Rabalski | Emergence and potential transmission route of avian influenza A (H5N1) virus in domestic cats in Poland, June 2023[END_REF] . However, it also indicates that undetected exposure of privately-owned cats to the virus could be frequent, consistent with serological evidence of avian influenza A infections in cats from different countries including household and shelter cats in South Korea [START_REF] Jeoung | Seroprevalence of subtype H3 influenza A virus in South Korean cats[END_REF][START_REF] Zhao | Serological screening of influenza A virus antibodies in cats and dogs indicates frequent infection with different subtypes[END_REF] . Finally, if the virus is spread to cats through other routes (e.g. hunting and ingestion of infected birds by stray or privatelyowned cats with outdoor access), the ability to establish plausible and specific epidemiological links would be challenged by the difficulty of conducting timely and targeted sampling as well as comprehensive history taking. While inadequately processed uncooked poultry meat leftovers in Shelter 2 were successfully collected and tested, it remains uncertain if the same could be achieved in other scenarios. This is exemplified by the recent influenza A(H5N1) infections of cats from individual households in Poland, where purchased food could only be tested for suspected cases, but not for confirmed cases [START_REF] Rabalski | Emergence and potential transmission route of avian influenza A (H5N1) virus in domestic cats in Poland, June 2023[END_REF] .

The influenza A(H5N1) outbreaks in the cat shelters in South Korea, along with an increasing number of reports of influenza A(H5N1) infection in mammals [START_REF] Offlu | OFFLU Call to Discuss Avian Influenza Events in Mammals[END_REF][START_REF] Lindh | Highly pathogenic avian influenza A(H5N1) virus infection on multiple fur farms in the South and Central Ostrobothnia regions of Finland, July 2023[END_REF][START_REF] Rabalski | Emergence and potential transmission route of avian influenza A (H5N1) virus in domestic cats in Poland, June 2023[END_REF] , suggest the need to enhance the effectiveness of infectious disease surveillance and prevention in any settings where a group of potentially susceptible animals are kept in close contact. This is particularly important for groups of animals that typically are not covered by regulatory efforts aimed at maintaining or improving animal health and welfare standards. These animal groups could not only provide environments for cross-species viral transmission, promoting zoonotic risk, but could also serve as sentinels for detecting such events, thereby offering opportunities to assess and then mitigate such risk. Several strategies can be implemented:

Firstly, it is important to require the aforementioned settings to record adverse animal health events at individual (e.g. clinical signs) and group levels (e.g. baseline mortality and morbidity), along with environmental factors (e.g. access to/from wildlife, and introduction of new animals) and husbandry conditions (e.g. food and water source), in systematic ways. In the event of cross-species viral transmission, this information will help to better understand the source of infection and thus inform the implementation of preventive and control measures. Such a recording practice appears to have been lacking in these particular settings, very much in contrast to conventional livestock farming where the recording is routinely practised.

Secondly, regularly training staff in the aforementioned settings to report any unusual clinical signs or trends is crucial for timely and sensitive early detection, coupled with the above recording practice. For this, animal health authorities should define clear reporting criteria, ensure their staff's familiarity with these criteria, and work to minimise the risk of underreporting due to potential stigmatisation. Additionally, animals in these settings need to be regularly examined by veterinarians to aid the timely recognition of unusual health events, which are often neglected due to economic constraints. Importantly, animal health authorities could play a role by designating veterinary staff to provide regular trainings to the staff about the recording practice and reporting criteria and to examine the animals.

Thirdly, the identification of inadequately processed uncooked poultry meat as a potential common source of influenza A(H5N1) infection in cats in both South Korea and Poland provides strong justification for prohibiting or limiting feeding of uncooked meat to animals kept for non-conventional production purposes and those in non-agricultural settings, in order to minimise the risk of cross-species transmission of influenza A(H5N1) virus and other viruses. Given the widespread availability of heat-treated commercial pet foods and the option to cook raw meat before feeding, this recommendation might be feasible for most animal species in these settings. Furthermore, if necessary, a ban on feeding uncooked meat to certain animal species could be implemented where cross-species transmission has been already reported or the risk is considered high (e.g. uncooked poultry meat to cats, minks, and foxes), similar to the bans on swill feeding in many countries to prevent the introduction of African swine fever virus into domestic pig farms [START_REF] Guinat | Transmission routes of African swine fever virus to domestic pigs: current knowledge and future research directions[END_REF] . Finally, there is a need for continued discussion on how to implement measures to prevent and control crossspecies viral transmission. It is crucial to involve all relevant stakeholders in this discussion, particularly the staff of the aforementioned animal settings, as their understanding of the implications of animal keeping for animal and human health might be less than amongst those involved in conventional livestock farming.

In conclusion, the recent influenza A(H5N1) outbreaks in South Korean cat shelters illustrate the risk of cross-species viral transmission in animals kept for non-agricultural or non-conventional livestock farming purposes, considered to present potential threats to human health. These events emphasise the need to strengthen surveillance of cross-species viral transmission events within these specific animal populations. However, it is also important to acknowledge that such efforts would require supplementary resources for national animal disease surveillance systems. While the scale of these additional resources may be relatively modest compared to those already invested in conventional livestock health surveillance, it could still pose a significant economic burden, especially in regions where the animal disease surveillance system is already poorly resourced. Therefore, it will be crucial to set realistic priorities by conducting risk assessments on the interfaces at which cross-species transmission has already been detected or expected to occur, in order to allocate limited surveillance resources based on the outcome of these risk assessments. By adopting such approaches, we can better prepare to protect against future zoonotic threats, thereby safeguarding both human and animal populations globally.

Younjung Kim 1,2 , Guillaume Fournié 3,4,5 , Raphaëlle Métras 1 , Daesub Song 6 , Christl A. Donnelly [START_REF] Lindh | Highly pathogenic avian influenza A(H5N1) virus infection on multiple fur farms in the South and Central Ostrobothnia regions of Finland, July 2023[END_REF][START_REF] Oreshkova | SARS-CoV-2 infection in farmed minks, the Netherlands, April and May 2020[END_REF][START_REF] Peacock | Mink farming poses risks for future viral pandemics[END_REF] , Dirk U. Pfeiffer Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2023

  Comment https://doi.org/10.1038/s41467-023-42738-w Lessons for cross-species viral transmission surveillance from highly pathogenic avian influenza Korean cat shelter outbreaks Younjung Kim, Guillaume Fournié, Raphaëlle Métras, Daesub Song, Christl A. Donnelly, Dirk U. Pfeiffer & Pierre Nouvellet Check for updates

  [START_REF] Li | Bats are natural reservoirs of SARS-like coronaviruses[END_REF][START_REF]Human Infection with Avian Influenza A(H5) Viruses[END_REF] & Pierre Nouvellet[START_REF] Parrish | Cross-species virus transmission and the emergence of new epidemic diseases[END_REF][START_REF] Peacock | Mink farming poses risks for future viral pandemics[END_REF] Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

	Comment
	nature communications	(2023) 14:6958 |

1 Sorbonne Université, INSERM, Institut Pierre Louis d'Épidémiologie et de Santé Publique (IPLESP), UMRS 1136 Paris, France. 2 Department of Ecology and Evolution, School of Life Sciences, University of Sussex, Brighton and Hove, UK. 3 Department of Pathobiology and Population Sciences, Royal Veterinary College, London, UK. 4 Université de Lyon, INRAE, VetAgro Sup, UMR EPIA, Marcy l′Etoile, France. 5 Université Clermont Auvergne, INRAE, VetAgro Sup, UMR EPIA, Saint-Gènes-Champanelle, France. 6 Department of Veterinary Medicine Virology Laboratory, College of Veterinary Medicine and Research Institute for Veterinary Science, Seoul National University, Seoul, Republic of Korea. 7 Department of Statistics, University of Oxford, Oxford, UK. 8 Pandemic Sciences Institute, University of Oxford, Oxford, UK. 9 MRC Centre for Global Infectious Disease Analysis and Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, UK. 10 City University of Hong Kong, Hong Kong SAR, China.

e-mail: younjung.kim@inserm.fr

Acknowledgements

We would like to express our gratitude to Professor Mika Salminen, the Director of the Department of Public Health and Welfare at the Finnish Institute for Health and Welfare, for providing valuable feedback on the manuscript.

Author contributions

Competing interests

The authors declare no competing interests.


Xudong Fan
email: fanxudong@njust.edu.cn

Yifan Zhu

Zihao Su

Ning Li

Xiaolong Huang

Yang Kang

Can Li

Chunsheng Weng

Hui Zhang
email: seuzhanghui@seu.edu.cn

Weiwei Kan
email: ‡kan@njust.edu.cn

Badreddine Assouar
email: badreddine.assouar@univ-lorraine.fr

Transverse Particle Trapping Using Finite Bessel Beams based on Acoustic Metamaterials

We investigate the transverse trapping force acting on a small particle on/off the central axis of zero-order finite Bessel beams. Combining the simulated fields with the Gorkov force potential, the transverse trapping behaviors on small objects are analyzed, and the reversal of the trapping behaviors is recovered when varying the paraxiality parameter of the Bessel beam. The results prove the possibility of using axisymmetric Bessel beams to trap both dense and stiff particles as well as light and soft ones. The particles can be trapped at the maximum central pressure in the main lobe and also the maximum pressure of the other transverse locations. A lossy acoustic metastructure with the ability to decouple the phase and amplitude modulations is used to generate the desired sound field, which is used to trap a foam ball as an example. Our research opens a promising avenue to design and develop simplified acoustic tweezers.

I. INTRODUCTION

Acoustic waves, as one of the most important forms in the classical wave system, play a significant role in the development of science and technology. When an object is placed in an acoustic field, there exists an acoustic radiation force acting on it. The force originates from the momentum transfer from the field to the object due to the scattering, reflection, and absorption. The acoustic radiation force acts throughout the object, but owing to the overall momentum conservation, the radiation force can be reduced to an integration of the time-averaged momentum-flux tensor over an arbitrary closed surface enclosing the whole object. [START_REF] Sarvazyan | Biomedical applications of radiation force of ultrasound: historical roots and physical basis[END_REF] Acoustic radiation forces have been studied for a long time in regards to the sound waves of different forms. [START_REF] Gor'kov | On the forces acting on a small particle in an acoustical field in an ideal fluid[END_REF][START_REF] Wu | Acoustical tweezers[END_REF][START_REF] Marston | Axial radiation force of a Bessel beam on a sphere and direction reversal of the force[END_REF][START_REF] Zhang | Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres[END_REF][START_REF] Zhang | Axial radiation force exerted by general non-diffracting beams[END_REF][START_REF] Xu | Transversally stable acoustic pulling force produced by two crossed plane waves[END_REF][START_REF] Courtney | Dexterous manipulation of microparticles using Bessel-function acoustic pressure fields[END_REF][START_REF] Démoré | Acoustic tractor beam[END_REF][START_REF] Marzo | Holographic acoustic elements for manipulation of levitated objects[END_REF][START_REF] Melde | Holograms for acoustics[END_REF][START_REF] Marzo | Realization of compact tractor beams using acoustic delay-lines[END_REF][START_REF] Marzo | Acoustic virtual vortices with tunable orbital angular momentum for trapping of mie particles[END_REF][START_REF] Zhang | Reversals of orbital angular momentum transfer and radiation torque[END_REF][START_REF] Fan | Trapping force of acoustical bessel beams on a sphere and stable tractor beams[END_REF][START_REF] Fan | Phase shift approach for engineering desired radiation force: Acoustic pulling force example[END_REF][START_REF] Korozlu | Acoustic sorting of airborne particles by a phononic crystal waveguide[END_REF] The trapping behaviors generated by standing waves on small objects (object sizes are much smaller than the wavelength) have been well understood, [START_REF] Gor'kov | On the forces acting on a small particle in an acoustical field in an ideal fluid[END_REF] where relatively light and soft particles (like droplets) are trapped to the pressure maximum (anti-node), yet relatively dense and stiff particles (like elastic objects) would be trapped to pressure minimum (node). On the other hand, the recent studies on acoustic radiation forces based on non-diffracting beams [4-6, 14, 15, 18-20] have predicted the possibility for particle manipulations with more flexibility. However, in practical situations and applications, non-diffracting beams, such as acoustic approach for field manipulations. [START_REF] Li | Reflected wavefront manipulation based on ultrathin 351 planar acoustic metasurfaces[END_REF][START_REF] Zhao | Manipulating 354 acoustic wavefront by inhomogeneous impedance and 355 steerable extraordinary reflection[END_REF][START_REF] Zhang | Generation of acoustic 359 self-bending and bottle beams by phase engineering[END_REF][START_REF] Li | Experimental realization 363 of full control of reflected waves with subwavelength 364 acoustic metasurfaces[END_REF][START_REF] Tang | Anomalous refraction of airborne sound through 368 ultrathin metasurfaces[END_REF][27][START_REF] Li | Metascreen-based acoustic passive phased 375 array[END_REF][START_REF] Ma | Acoustic metamaterials: From 377 local resonances to broad horizons[END_REF][START_REF] Cummer | Controlling 380 sound with acoustic metamaterials[END_REF][START_REF] Zhu | Implementation of dispersion-free slow 384 acoustic wave propagation and phase engineering 385 with helical-structured metamaterials[END_REF][START_REF] Jiang | Convert acoustic resonances to orbital 389 angular momentum[END_REF][START_REF] Fan | Broadband convergence of acoustic energy with 393 binary reflected phases on planar surface[END_REF][START_REF] Zhu | Ultrathin acoustic metasurface-based schroeder diffuser[END_REF][START_REF] Li | Tunable asymmetric transmission via lossy acoustic metasurfaces[END_REF][START_REF] Zhu | Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase[END_REF][START_REF] Assouar | Acoustic metasurfaces[END_REF][START_REF] Fan | Illusion for airborne sound source by a closed layer with subwavelength thickness[END_REF][START_REF] Fan | Acoustic orbital angular momentum hall effect and realization using a metasurface[END_REF] Acoustic 65 metamaterials can achieve extraordinary properties and 66 phenomena, which natural materials would be difficult 67 to achieve, such as negative refraction/reflection, [START_REF] Li | Reflected wavefront manipulation based on ultrathin 351 planar acoustic metasurfaces[END_REF][START_REF] Zhao | Manipulating 354 acoustic wavefront by inhomogeneous impedance and 355 steerable extraordinary reflection[END_REF] 68 cloaking, [START_REF] Zhang | Broadband acoustic cloak for ultrasound waves[END_REF][START_REF] Zhu | Acoustic cloaking by a superlens with single-negative materials[END_REF][START_REF] Jiang | Broadband field rotator based on acoustic metamaterials[END_REF][START_REF] Kan | Three-dimensional broadband 430 acoustic illusion cloak for sound-hard boundaries of 431 curved geometry[END_REF][START_REF] Gao | Non-blind acoustic invisibility by dual 434 layers of homogeneous single-negative media[END_REF] hologram, [START_REF] Melde | Holograms for acoustics[END_REF][START_REF] Zhu | Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase[END_REF][START_REF] Inoue | Acoustical boundary hologram for 438 macroscopic rigid-body levitation[END_REF][START_REF] Zhu | Systematic design of 441 multiplexed-acoustic-metasurface hologram with 442 simultaneous amplitude and phase modulations[END_REF][START_REF] Zhu | Systematic design and experimental demonstration of 447 transmission-type multiplexed acoustic metaholograms[END_REF] and specific 69 field generations. [START_REF] Li | Reflected wavefront manipulation based on ultrathin 351 planar acoustic metasurfaces[END_REF][START_REF] Zhang | Generation of acoustic 359 self-bending and bottle beams by phase engineering[END_REF][START_REF] Jiang | Convert acoustic resonances to orbital 389 angular momentum[END_REF] 70

In this work, we investigate the transverse acoustic The force potential U is then obtained based on the simulated pressure p and velocity fields v, [START_REF] Gor'kov | On the forces acting on a small particle in an acoustical field in an ideal fluid[END_REF] i.e.,

U = (πa 3 /3)[f 1 |p| 2 /(ρ 0 c 2 0 ) -(3/2)f 2 ρ 0 |v| 2 ], ( 2
)
where a is the radius of the object, ρ 0 and c 0 are the mass density and the sound speed of the background medium, and f 1 and f 2 are the monopole and dipole factors depending on the mass density ratio and bulk modulus ratio between the object and the surrounding medium.

[15] Here, rigid particles with f 1 = 1 = f 2 were used in the calculation since for most solid objects, the density and bulk modulus are much larger than the background medium, air, so the results here are applicable to most elastic objects. Like plane waves, an ideal Bessel beam cannot be created since it requires an infinitely large source and also an infinite amount of energy. Hence, the approximated Bessel beams only exist within a certain spatial range.

We examine the relationship between the approximated spatial range R with the angle β [see red dots in Fig. 2(d)], where the spatial range R for each angle modulation of the amplitude A and the phase Φ, [START_REF] Zhu | Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase[END_REF] i.e.,

A = d 4 -w 4 d 4 + w 4 , Φ = - 4πh 1 λ . (4)
The decoupled modulation of the amplitude and the phase allows for all the combinations in their full parameter ranges [that is, A ∈ [0, 1] and Φ ∈ [0, 2π]; see

71

  radiation force generated by finite Bessel beams based 72 on acoustic metamaterials. The transverse trapping 73 behaviors of a small particle on/off the central axis of the 74 Bessel beams are studied numerically and experimentally.75 A lossy acoustic metastructure, capable of decoupling 76 the phase and amplitude modulations, is designed to 77 generate the desired Bessel field, which is then used to 78 trap a small foam ball to the beam center as an example. 79 Our work gains insight into some unusual and unique 80 trapping behaviors, which will help the further study 81 of particle manipulations using acoustic radiation forces 82 and acoustic Bessel fields.

FIG. 1 .

 1 FIG. 1. Illustration of transverse particle trapping by acoustic Bessel beams.

FIG. 2 .

 2 FIG. 2. Reversal of transverse particle trapping behaviors when reducing the angle from (a) β = 40 • to (b) β = 15 • . Black solid lines: normalized squared pressure, |p| 2 , at z = 3λ; red dots: normalized force potential U computed from Eq. (2) based on the simulated pressure and velocity fields. Insets: two-dimensional normalized squared pressure (color plots) and the corresponding radiation forces (white arrows). (c) Variation of the first trapping location r0 near the beam axis. Transition angle happens at β ∼ 29 • . (d) Spatial range R for approximated Bessel beams from a finite sound source. Red dots: simulated results obtained based on the -3dB location in the z direction; black line: curve fitting, R ≈ 0.9H/ tan β with H being the half length of the finite source.

FIG. 3 .Fig. 3 (FIG. 4 .

 334 FIG. 3. (a) Illustration of one element of the artificial structure. Parameters are chosen as h = λ, D = 0.25λ, d = 0.8D, h2 = 0.5λ, and h = h1 + h2 + h3. λ is the wavelength. By adjusting the geometry parameters w and h1, (b) the amplitude and (c) the phase of the reflected field could be modulated separately [Eq. (4)]. (d) The artificial structure used in the simulation for β = 15 • , and the corresponding geometry parameters w (black circles) and h1 (red dots) for the 40 elements.

Fig. 3 (

 3 Fig. 3(b) and (c)], which is necessary to generate acousticBessel beams in our case. The viscosity effect of the metastructure here can be ignored since the boundary layer thickness is much smaller than the width of the elements.[START_REF] Ward | Boundary-layer effects 451 on acoustic transmission through narrow slit cavities[END_REF][START_REF] Molerón | Visco-thermal effects in acoustic metamaterials[END_REF] The cross-section of the structure and the corresponding geometry parameters w and h 1 for the 40 elements are shown in Fig.3(d), which would be used to generated an zero-order Bessel beam with β = 15 • .The measured and simulated fields |p| 2 generated via the acoustic metastructure are shown in Fig.4(a). The results are further compared with the field generated by an ideal continuously distributed Bessel source of the same size. We have examined the transverse profile of the field at z = 12λ (white dashed lines). From the results, one can find the fields generated via the acoustic metastructure (green diamonds and blue circles) agree pretty well with the ideal source of the same size (red dots), and both of them follow the squared zero-order Bessel function (black solid line). Hence, with the aid of this structure, the zero-order Bessel beam is effectively generated and can be utilized for particle manipulations.As an example, the transverse particle trapping behavior on a small foam ball (character size of ∼ 2 mm) has been examined and experimentally observed, where the particle is transversely trapped to the center of the field, see Fig.4(b). Here, the sample of the metastructure is fabricated using a 3D printer (Wiiboox Four) with the material PLA. The printing resolution is 0.1mm. A signal generator (RIGOL DG1032) and a power amplifier (CROWN XLi2500) are connected to a loudspeaker with a rated power of 100 W (Lutiane DL-630). The working frequency is 17 kHz, corresponding to the wavelength λ ∼

  274

from total transmission to total reflection and high 456 absorption," New Journal of Physics 18, 033003 (2016).