Zhixin Dai

Fabio Galeotti

Marie Claire Villeval

P Jacquesson

R Sauter

D Aubaret

L Clerc

S Belhadj

L Charroin

A Solda

The Efficiency of Crackdowns: A Lab-in-the-Field Experiment in Public Transportations

Keywords: Crackdowns, fraud, risk, monitoring, transportation, field experiment JEL codes: C91, D83, K42 Crackdowns, fraud, risk, monitoring, transportation, field experiment JEL Classification Codes: C91, D83, K42

The concentration of high frequency controls in a limited period of time ("crackdowns") constitutes an important feature of many law-enforcement policies around the world. In this paper, we offer a comprehensive investigation on the relative efficiency and effectiveness of various crackdown policies using a lab-in-the-field experiment with real passengers of a public transport service. We introduce a novel game, the daily public transportation game, where subjects have to decide, over many periods, whether to buy or not a ticket knowing that there might be a control. Our results show that (a) concentrated crackdowns are less effective and efficient than random controls; (b) prolonged crackdowns reduce fare-dodging during the period of intense monitoring but induces a burst of fraud as soon as they are withdrawn; (c) pre-announced controls induces more fraud in the periods without control. Overall, we also observe that real fare-dodgers fraud more in the experiment than non-faredodgers.

Introduction

A crackdown -i.e. the concentration of high-frequency or systematic controls in a limited amount of time and/or on a delimited geographical area or subset of the population -is a type of policy intervention widely used by law-enforcement institutions to fight against crime [START_REF] Sherman | Police Crackdowns: Initial and Residual Deterrence[END_REF]Di Tella andSchargrodsky, 2002, 2004;[START_REF] Kleiman | The dynamics of deterrence[END_REF][START_REF] Eeckhout | A theory of optimal random crackdowns[END_REF][START_REF] Van Der Weele | Beyond the state of nature: Introducing social interactions in the economic model of crime[END_REF]. It was one of the most important policing policies in the U.S [START_REF] Sherman | Police Crackdowns: Initial and Residual Deterrence[END_REF] as well as in China in the 1980s [START_REF] Schultz | Economic Crimes in the People's Republic of China: A Swinging Door Policy[END_REF], and has still great relevance worldwide. Its applications include tax audits [START_REF] Slemrod | Taxpayer response to an increased probability of audit: Evidence from a controlled experiment in Minnesota[END_REF][START_REF] Kleven | Unwilling or unable to cheat?: evidence from a tax audit experiment in Denmark[END_REF], traffic enforcement [START_REF] Eeckhout | A theory of optimal random crackdowns[END_REF], corruption and theft (Di Tella andSchargrodsky, 2003, 2004), drug markets [START_REF] Farrell | Where have all the flowers gone? Evaluation of the Taliban crackdown against opium poppy cultivation in Afghanistan[END_REF], and urban violence [START_REF] Moeller | Police crackdown on Christiania in Copenhagen[END_REF]. It is also frequently used in public transportations to discourage fare-dodging.

Several economic theories have modeled the advantages of employing crackdown policies [START_REF] Lando | The advantage of focusing law enforcement effort[END_REF][START_REF] Lazear | Speeding, terrorism, and teaching to the test[END_REF][START_REF] Eeckhout | A theory of optimal random crackdowns[END_REF].

These studies show that if the relationship between crime and expected punishment is concave, crackdowns will outperform a randomly distributed control strategy; if it is convex, then the opposite will hold. These models also demonstrate that crackdowns should be pre-announced in order to maximize their deterrent effect, especially to modify the behavior of those who have the highest cost of effort. From an empirical perspective, it is however hard to measure the shape of the relationship between crime and expected punishment using field data. In addition, the evaluation of pre-announced crackdowns is usually based on their immediate effects while they may also have effects in the long run. These long-term effects may be deleterious if more crimes are induced as soon as a crackdown ends; they may be positive if a high risk of control has an educative effect.

Empirical studies, such as [START_REF] Kastlunger | Sequences of audits, tax compliance, and taxpaying strategies[END_REF], Di Tella and Schargrodsky (2003,2004), Dai et al. (2015c), [START_REF] Banuri | Cracking down on bribery[END_REF] offer mixed evidence on the effectiveness and efficiency of crackdowns. Moreover, they do not investigate the relative efficiency and effectiveness of crackdowns to alternative mechanisms of crime prevention such as non-concentrated random controls keeping everything else constant. 1 Without a suitable comparison test, it is difficult to discern the real capacity of crackdown policies from these studies.

To fill this gap, we conducted an artefactual field experiment [START_REF] Harrison | Field experiments[END_REF]) using passengers of the public transport service in Lyon, the third largest city in France. We look at small-scale cheating of ordinary people which, quite contrary to what one would expect, has the largest social and economic impact for society [START_REF] Bucciol | Unethical behavior in the field: Demographic characteristics and beliefs of the cheater[END_REF][START_REF] Mazar | Dishonesty in everyday life and its policy implications[END_REF]. More precisely, we investigate fare evasion. 2 According to some recent statistics, fare-dodging caused € 300 million loss to the French national railway company and € 100 million to the Parisian public transport operator in 2013 (Lefigaro.fr, 2013). It is not a problem circumscribed to France but it is widespread in all countries [START_REF] Bonfanti | Human factors reduce aggression and fare evasion[END_REF]. It is thus important to determine which and to what extent crackdown policies are effective and efficient to fight against fare evasion.

To investigate the relative efficiency and effectiveness of various crackdown policies we propose a novel game called the daily public transportation game. In this laboratory game, participants have to decide repeatedly (i.e. over many periods) whether to buy or not a (experimental) bus ticket knowing that there is a risk of control. We study how compliance behavior evolves over time depending on subjects' exposure to either repeated controls concentrated in a given period of time (crackdown) or irregular controls spread out over time. We analyze behavior during and after periods of control to investigate the immediate/short-term and long-term effects of these policies. We also test whether it is more effective to introduce

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1 ! These studies either did not explicitly compare the efficiency and effectiveness of a crackdown policy to an alternative mechanism of crime prevention such as random controls (Di Tella andSchargrodsky, 2003, 2004;[START_REF] Banuri | Cracking down on bribery[END_REF] or they vary at the same time other things than just the concentration of controls (Dai et al., 2015c;[START_REF] Kastlunger | Sequences of audits, tax compliance, and taxpaying strategies[END_REF]. For instance, Dai et al. (2015c) also vary the total number of audits, while [START_REF] Kastlunger | Sequences of audits, tax compliance, and taxpaying strategies[END_REF] indirectly change subjects' expectation of an audit by informing them in advance of the overall probability of being audit.! 2 The cost of using a public vehicle is, in general, quite small (the price of a ticket is € 1.70 in the city where this study was conducted). It thus seems appropriate to classify fare dodging as a case of small-scale cheating.

crackdowns at an early or later stage of the game, and whether crackdowns should be pre-announced ex ante or not (i.e. whether or not subjects should be informed in advance of a control).

With respect to the latter comparison, our experiment also contributes to the literature on the efficiency of sanction mechanisms under ambiguity.3 Indeed, when crackdowns are not pre-announced, subjects do not know whether there will be a control or not and what is the probability of its occurrence (i.e. condition of uncertainty). We therefore contribute to the study of the effects of ambiguity on behavior in the loss domain, whereas the impact of ambiguity is much more frequently studied in the gain domain. In contrast, when crackdowns are announced in advance, subjects are fully informed about whether a control will occur (i.e. condition of certainty). By comparing these alternative conditions, we can investigate whether uncertainty favors compliance or not.

An additional originality of our study is that we ran our experiment with a non-standard subject pool consisting of passengers of the public transport. This enables us to test different crackdown policies with a representative sample of the people for which these policies can be directly relevant. 4 In addition, we are able to identify real fare-dodgers by verifying whether subjects can present a validated ticket at the end of the experiment and by asking subjects to self-report how often they travel without a valid ticket in their real life. This allows us to compare the behavior of actual fare-dodgers and non-fare-dodgers in our game, and to test whether our game captures important dimensions of actual behavior in the field. Hence, our study also contributes to the general discussion about whether experimental results can be generalized to the real world (for a recent overview on this topic, see Fréchette and Schotter, 2015).

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To give a very brief preview of our findings, in the presence of ambiguity on audits (and thus on sanctions), random controls which are spread out over time are more effective at reducing fare-dodging in the laboratory than crackdowns, and this effect is even stronger for real-world fare-dodgers. We also find that a more prolonged crackdown reduces fare-dodging during the period of intense monitoring but induces a burst of fraud as soon as it ends. Furthermore, pre-announced controls induce more fraud in the periods without control. Compared to non-concentrated random controls, crackdowns have a positive impact on compliance but only in the short run. However, they entail potentially deleterious effects in the long run since, after a crackdown is over, fraud rate increases to levels that are even higher than before the introduction of the crackdown even when crackdowns are not pre-announced and individuals do not know the total number of audits. Finally, we find that real fare-dodgers cheat more in all treatments compared to non-fare-dodgers.

In the remainder of our paper, Section 2 surveys the related literature. Section 3 describes the experimental design and procedures. Section 4 reports the experimental findings while Section 5 discusses the results and concludes.

Related studies

Theoretical studies have shown the advantages of crackdowns [START_REF] Lando | The advantage of focusing law enforcement effort[END_REF][START_REF] Lazear | Speeding, terrorism, and teaching to the test[END_REF][START_REF] Kleiman | The dynamics of deterrence[END_REF]Eeckout et al., 2010). These papers mainly focus on when crackdowns are optimal to use. The models by [START_REF] Lazear | Speeding, terrorism, and teaching to the test[END_REF] and [START_REF] Eeckhout | A theory of optimal random crackdowns[END_REF] are more germane to our experimental setting as they focus on systematic controls in a limited amount of time or delimited geographical area. 5Their results rely on the shape of the relationship between crime and expected punishment. In particular, concentrating the enforcement resources in a specific area or period of time is predicted to generate a greater reduction in crime than spreading the same resources over a broader area or longer period of time but only when the relationship between crime and expected punishment is concave. When the opposite is

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true (i.e. the relationship is not concave), a less concentrated control policy is more effective. It is however difficult to test these models empirically since the shape of the relationship between crime and expected punishment cannot be easily identified in real settings. Our results can indirectly shed light on this relationship: if crackdowns are more efficient than less concentrated controls, we may infer that the relationship between crime and expected punishment is concave. Some empirical studies have investigated the efficiency of crackdown policies.

Di [START_REF] Di Tella | The Role of Wages and Auditing during a Crackdown on Corruption in the City of Buenos Aires[END_REF] showed that the prices paid by hospitals for basic and homogenous inputs decreased by 15% during the first 9 months of a crackdown.

In a natural experiment, Di Tella and Schargrodsky (2004) found a large deterrent effect on car thefts once police protection had increased after a terroristic attack. In these two studies, the measure of efficiency is however imprecise for several reasons.

First, the total enforcement input is unknown. Second, there may be other changes during the crackdown period that may affect behavior. For example, in Di Tella and [START_REF] Di Tella | The Role of Wages and Auditing during a Crackdown on Corruption in the City of Buenos Aires[END_REF] the evolution of wages may also play a role in limiting corruption, and, therefore, the pure effect of the crackdown cannot be totally isolated [START_REF] Banuri | Cracking down on bribery[END_REF].

We are only aware of three experimental studies explicitly related to crackdowns. They show that crackdowns impact, if anything, only in the short run, and have no effect or even a deleterious one in the long run. The first study by [START_REF] Kastlunger | Sequences of audits, tax compliance, and taxpaying strategies[END_REF] examines the impact of various sequences of audits on tax compliance when subjects know the probability of audits but not their distribution over time. They show that! the decrease of compliance after an audit is caused more by misperception of chance than by the willingness to repair a loss. In contrast, Dai et al. (2015c) investigate compliance under ambiguity when subjects ignore not only the distribution of audits over time but also the overall probability of audits. Their vehicle of research is a public good game with a centralized mechanism of punishment that sanctions, with a certain probability, subjects who contributed less than the average group contribution. The results indicate that even under ambiguity, the contribution level is the same under a continuous audit regime (in which the -unknownprobability of being punished is equal to 1) compared to a random audit regime (in which the probability of being punished is equal to 1/3 but with a fine coefficient three times higher). Interestingly, the results also show that contributions were significantly lower in the former than in the latter regime after audits were completely removed. This suggests that when individuals are not informed on the risk of being audited, crackdowns may be less efficient than more irregular audits because subjects are less able to update their beliefs when audits are more irregular.

The third experimental study is [START_REF] Banuri | Cracking down on bribery[END_REF]. The authors use a bribery laboratory experiment to investigate whether a crackdown has long-term effects on compliance. Crackdowns were introduced in the second of three ten-period blocks. By comparing the corruption levels in the pre-crackdown block with the post-crackdown block, the authors found no significant difference. They therefore conclude that short-term crackdowns are largely ineffective in changing behavior in the long run.

Compared to the previous studies, the current study allows us not only to compare the relative efficiency and effectiveness of various crackdown policies but also to study the impact of reintroducing a crackdown, the length and the timing of a crackdown, and the consequence of combing crackdowns with random controls. In addition, it enables us to investigate the role of pre-announcement in both crackdown and random-control policies. On this respect, theoretical papers suggest that crackdowns should be pre-announced to deter illegal behaviors [START_REF] Lazear | Speeding, terrorism, and teaching to the test[END_REF][START_REF] Kleiman | The dynamics of deterrence[END_REF]Eeckout et al., 2010). However, to the best of our knowledge, there is no systematic study that investigates the short-run and long-run implications of pre-announcing or not a crackdown. 6 Finally, our study enables us to 6 We acknowledge that there are a few studies in the literature on tax evasion that investigate the effect of sending threat-of-audit letters (e.g. [START_REF] Slemrod | Taxpayer response to an increased probability of audit: Evidence from a controlled experiment in Minnesota[END_REF][START_REF] Kleven | Unwilling or unable to cheat?: evidence from a tax audit experiment in Denmark[END_REF][START_REF] Fiorio | Taxpaying response of small firms to an increased probability of audit: some evidence from Italy[END_REF]. What is usually found is that informing people about the audit activity has a positive and statistically significant effect on tax fraud compliance. More relevant for us is the study of [START_REF] Alm | Getting the word out: Enforcement information dissemination and compliance behavior[END_REF] who investigated, by means of a lab experiment, different ways in which information regarding the audit activity can be transmitted ex-ante and ex-post to the taxpayers. They ran sessions where the measure the impact of different law-enforcement policies using real-world subjects for whom these policies may be directly relevant in their everyday life.

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Experimental design and procedures

Experimental design

The experiment is divided in five different parts. In the first part, we elicited participant's attitudes towards risk and ambiguity both in the domain of gains and in the domain of losses. In the second part, we measured subjects' tendency to behave dishonestly by asking them to privately roll a dice and report the outcome (a task similar to the one used in Fischbacher and Föllmi-Heusi, 2013). In the third part, we measured the tendency to behave dishonesty in a contextualized laboratory task which was described as a decision on whether to buy or not a ticket for using public transportation and covering different trip lengths. 7 The fourth part was what we refer to as the daily public transportation game which is the main focus of this paper and is described in detail below. The final part was a socio-demographic questionnaire which was administered to the subjects at the end of the experiment. A detailed description of the second and third parts, together with their main results, are reported in a companion paper [START_REF] Dai | Cheating in the lab predicts cheating in the field! An experiment in public transportations[END_REF]. No feedback or information about future tasks was given to subjects in parts 1-3. In addition, all subjects went through the same parts (in the same order), and, therefore, earlier tasks could not explain across-treatment differences in the daily public transportation game.

Elicitation of attitudes towards risk and ambiguity. We elicited the participants' risk attitudes using a task developed by [START_REF] Eckel | Men, women and risk aversion: Experimental evidence[END_REF] and adopting a similar visual representation as [START_REF] Eckel | School environment and risk preferences: Experimental evidence[END_REF] and [START_REF] Cardenas | Risk attitudes and economic well-being in Latin America[END_REF].

Subjects made four consecutive lottery choices, first in the gain domain, then in the loss domain, next in the gain domain under ambiguity, and finally in the loss domain

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audit probability was pre-announced and sessions where it was not, and found that compliance was on average lower in the former. However, differently from our experiment, they did not consider periods of intense control (i.e. crackdowns). 7 We asked subjects to make several decisions under different audit probabilities and fines. under ambiguity. Every time the choice was displayed in a new screen. 8 Each choice consisted in selecting the most preferred of six possible lotteries. Table 1 displays the six lotteries for both the choices in the gain and loss domain. When the risk was known by the subjects, each lottery involved a 50/50 chance of a low or a high payoff.

Moving from Lottery 1 to Lottery 6, both expected return and risk (standard deviation) increase. Hence, subjects who are extremely risk-averse should choose the sure Lottery 1. Moderately risk-averse individuals should choose an intermediate lottery (Lotteries 2-4). Risk-neutral subjects should choose Lottery 5 or 6. Risk-seeking persons should choose Lottery 6. In the loss domain, lotteries could give negative payoffs. To prevent participants to make real losses in the experiment, we assigned subjects an initial endowment of € 40. This makes the expected payoffs equivalent in the loss and in the gain domains. Hence, the losses were only a framing manipulation.

Under ambiguity, the payoffs were the same as in the choices under certainty but the probability of each outcome was uncertain (between 3/10 and 7/10).

[Table 1 about here] The daily public transportation game. Each participant was initially endowed with € 35 to avoid a net loss in this game. To facilitate subjects' understanding of the experimental environment and enhance the external validity of our experimental setting in relation to the real-world environment where our subjects usually operated, we described the laboratory game as a choice on whether to pay or not a ticket for using a bus. 9 The game consists of 60 periods ("days") in total divided in 2 blocks of 30 days. For each day, participants were asked to decide whether or not buy a ticket to use a bus. The cost of a ticket was €1.70. 10 Subjects were told that a control of the ticket could occur in certain days. Subjects received no information on the number of audits and their distribution over time. If a participant was caught travelling without a

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The order in which subjects made their choices was kept fixed to facilitate decision-making and avoid confusion. 9 We however refrain from using strong terminology which could lead to experimenter demand effects. 10 This was also equivalent to the real cost of using a public transport in the French city where the experiment took place. ticket, he or she had to pay a fine of € 10 plus the price of the unpaid ticket (€ 11.70 in total); this was made common knowledge. At the end of each experimental day, subjects received an immediate feedback on whether they had been audited (or not) and fined. However, this information does not remain visible on the computer screen once the subject moves to the next day. This means that subjects have to memorize the previous sequence of audits. At the end of the task, three periods (days) were selected at random for actual payment.

The experiment consisted of 8 treatments. These are summarized in Table 2. In all treatments, we employed the same number of audits (12 in total). In the Random-Random treatment (RR), 6 audits were randomly distributed over the first block (days 1 to 30), and other 6 over the second block (days 31 to 60). In the Crackdown-Crackdown treatment (CC), we concentrated 6 consecutive audits in each block. In particular, subjects were audited in days 3 to 8 and 33 to 38. 11 To break the regularity of a crackdown's occurrence, we ran the Crackdown-Random treatment (CR), which is similar to the CC treatment except that, in the second block, audits were spread out as in the RR treatment. In the Random-Crackdown treatment (RC), we reversed this order by having random audits in the first block and a crackdown in the second block.

[Table 2 about here] In order to measure the impact of a longer crackdown policy, in the Early-Long-Crackdown treatment (C_Long1) we concentrated 12 consecutive audits in the first block, from day 3 to 14, and we applied no audit in the second block. To measure whether the timing of a crackdown matters, we also ran the Late-Long-Crackdown (C_Long2), where we applied the 12 consecutive audits in the second block from day 33 to 45.

As explained earlier, previous studies suggest that crackdowns should be [START_REF] Eeckhout | A theory of optimal random crackdowns[END_REF]. This motivates our last two treatments:

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Random-Random with pre-announcement (RR_A) and Crackdown-Crackdown with pre-announcement (CC_A). The treatments RR_A and CC_A are similar to the RR and CC treatments. The only difference is that subjects were informed in advance each day (i.e. before making a decision) whether an audit would occur this day.

In our setting, if subjects knew the exact audit probability -which is 20% given 12 audits across 60 periods -buying a ticket would be a dominant strategy.12 However, the audit probability is unknown. Rational and risk-neutral subjects should fraud if their perceived probability of audit is lower than 14.53%.

Experimental procedures

279 participants were recruited for a 45-minute experiment at the exit of the bus and tram in front of the main railway station of Lyon, the third largest city in France, between 11:00am and 6:30pm. Recruiters wore no uniform (to signal that they were not ticket inspectors). The recruiters invited passengers to participate in a study conducted by researchers of the university. People holding a monthly-pass were excluded (by definition, these persons are not fare-dodgers).

Recruiters informed passengers individually that the study would last between 45 and 60 minutes, they would earn between € 25 and € 75, on average € 50, and they would be paid immediately at the end of the experiment in vouchers which could be exchanged for goods and services in several places, including a near commercial center. They also indicated that all decisions were strictly anonymous and that no special knowledge was required. Once passengers agreed to participate, recruiters informed them to keep their ticket (if they had one) because it will be exchanged for a new free ticket at the end of the experiment to compensate them for the time spent in the lab.13

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We also recruited 35 subjects from the Fine Collection Office (FCO). These people did not pay immediately their fine after having being caught travelling without a ticket and they were issued a fine ticket to be paid later at the FCO. After they made their payment, recruiters used a similar procedure to invite them to participate in our experiment.

The experiment was conducted using our mobile laboratory in a building located near the recruitment point. Mobile partitions were used to isolate participants. Subjects made their decisions via tactile tablets. A maximum of 9 subjects participated at the same time in the laboratory. Since there was no interaction between participants during the experiment, subjects could start the experiment as soon as they arrived in the room.

Upon arrival and after signing a consent form, an experimenter randomly guided each participant to a workstation. Subjects were reminded that decisions were anonymous. All the instructions were displayed on the tablet. They were informed that they could raise their hand at any time and an experimenter would come to them and answer their questions privately.

Once a subject completed all the tasks, he or she was escorted to a separate payment room where he or she was paid in vouchers. Then we exchanged his or her validated ticket -if he or she had one -with a free day pass (providing a real incentive for exchanging a validated ticket).

Subjects on average completed the experiment in 37 minutes (12.81 of standard deviation) excluding the payment procedures. On average, participants earned about € 60 (20.59 of standard deviation). Earnings were calculated based on subjects' decisions in parts 1, 2 and either 3 or 4.

Identification of fare-dodgers

One major novelty of our study is the fact that we are able to measure the impact of different law-enforcement policies on actual fare-dodgers and non-fare-dodgers. Therefore, it is important to describe how we identified fare-dodgers and non-fare-dodgers.

We collected three different measures of fare-dodgers. First, we categorized as fare-dodgers subjects who were recruited at the FCO. Second, fare-dodgers were those subjects who could not display a validated ticket at the end of the experiment.

Finally, we classified as fare-dodgers those participants who, in the final questionnaire, self-reported to travel without a valid ticket at least once every 10 trips. 14 Note that we define a subject as fare-dodger if he or she fits in one or more of the three categories above. We believe this is a relatively reliable and comprehensive way to identify fare-dodgers for the following reasons. 15 First, we know for sure that subjects recruited at the FCO were fare-dodgers. Second, we can confidently say that subjects who could not display a valid ticket were fare dodgers since we recruited them when they were getting off the bus/tram and we explicitly told them to keep their ticket 16 . Hence, they were supposed to hold a validated ticket unless they fare dodged. Third, there is no reason why subjects who self-reported as fare-dodgers lied about this. 17 Of course, we recognize that our classification has some limitations and may not capture all the fare-dodgers who participated in our experiment. Some of them may have in fact bought the ticket on the day of the experiment and lied about their illegal behavior. 18 We should however point out that, if we accidentally classified some subjects as non-fare-dodgers, this would only strengthen our results if we find differences in behavior between the two groups (fare-dodgers and non-fare-dodgers).

To provide some summary statistics on our measures of fare-dodgers, excluding subjects from the FCO, 41.80% of the remaining participants could not show a 14 In the questionnaire, they were asked to report how often (from 0 to 10) they travel without a valid ticket out of 10 trips. 15 An alternative procedure would be that of relying only on one of the three measures. The risk is of course that of underestimate the number of fare dodgers. 16 The lab was also near the tram and bus stop (about 100 meters from the stop). 17 The opposite is likely to be true, that is subjects who self-reported as non-fare-dodgers were actually fare-dodgers. 18 We believe these are more likely to be occasional fare dodgers. validated ticket, 54.92% self-reported as fare-dodgers, 68.44% self-reported to be fare-dodgers and/or could not show a validated ticket, and 28.28% both self-reported as fare-dodgers and could not show a validated ticket. 19

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Experimental results

In this section, we first examine, both in aggregate and at individual level, the relative efficiency and effectiveness of our different treatments in terms of induced behavior, and whether fare-dodgers behave differently than non-fare-dodgers. We then compare the relative efficiency of the various crackdown policies in terms of revenue collected.

Relative efficiency and effectiveness of different treatments

Table 3 displays some summary statistics on the average fraud rate by treatment for actual fare-dodgers and non-fare-dodgers.

[Table 3 about here] One first important observation is that actual-fare-dodgers fraud more than non-fare-dodgers in all treatments and this difference is significant except in the RR and C_Long1 treatments (see the Test column in Table 3). This finding is important as it suggests that our experiment has some external validity.

Table 3 also indicates that the average fraud rate differs across treatments.

Straight comparisons of the fraud rates between treatments using non-parametric tests may, however, not be right. Since fare-dodgers behave differently than non-fare-dodgers, differences between treatments may in fact be explained by a different proportion of fare-dodgers rather than a change in behavior induced by the treatment manipulation.

Although the recruitment process was random, we indeed detect some variations in the participation of actual-fare-dodgers in each treatment, which may bias our

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19 These figures are consistent with data from the local public transport company (see, e.g., [START_REF] Keolis | Fraude: comment lutter?[END_REF], and other studies conducted in comparable countries [START_REF] Bucciol | Unethical behavior in the field: Demographic characteristics and beliefs of the cheater[END_REF]. Our high percentages are also due to the fact that we excluded people with a monthly pass from our experiment. measure of relative efficiency of crackdowns. 20 In order to control for this potential bias, we estimate a random-effects probit model with robust standard errors clustered at the individual level to account for the fact that the 279 players made 60 successive decisions. The dependent variable is a dummy which is equal to 1 if a subject chose to fraud on a given experimental day. Independent variables include a dummy variable for each treatment with RR taken as the reference category. The "Intensity Crackdown" variable indicates the consecutive number of audits occurred before the current day and captures the impact of crackdowns. We for whether a subject had been fined in the previous experimental day. In addition, we include measures of risk aversion in the gain and the loss domain with or without uncertainty. 21 Finally, we control for the behavior of fare-dodgers in two complementary ways. First, we include a dummy for fare-dodgers who did not display a valid ticket or self-reported as frauders. Second, we control, with a separate dummy, for the behavior of the fare-dodgers recruited at the FCO. We treat these latter fare-dodgers separately as their behavior is susceptible to be different from other fare-dodgers since they had just paid a fine.

[Table 4 about here]

In Table 4, Columns (1) and (2) report the results of the regression conducted on the data from the first block (days 1-30) and the second block (days 31-60) respectively, while Column (3) pools the data from the two blocks together. Columns (4-6) are identical to Columns (1-3) except that we only use data from actual fare-dodgers. In Columns (7-9), we only use data from non-fare-dodgers.

[Figure 1 about here] To help discussing the main results of Table 4, we also plot the fraud rate over time for each of our different treatments (Figure 1). For the sake of readability, we pool some days together. Precisely, we divide each block into four parts: 20 The number of actual fare-dodgers varies between 61% (C_Long1) to 79% (RR). 21 The higher the value, the less risk averse the subject is.

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pre-crackdown days (1-3, 31-33), crackdown days (4-9, 34-39), post-crackdown days (10)(11)(12)(40)(41)(42), and the remaining days (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(43)(44)(45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60). 22 Crackdown days are identified with a vertical line. In each panel of Figure 1, we always display the baseline condition (i.e. the RR treatment).

Table 4 shows that the probability of fraud is 14.2% higher in the CC treatment compared to the RR treatment. This also appears in Figure 1 where the average fraud rate of the CC treatment is always greater or similar to the average fraud rate of the RR treatment except during the second crackdown. Figure 1 (Panel A) also shows that, in the treatment, subjects almost did not react to the first crackdown but only to the second one as if there was a learning effect at work. Alternating crackdowns with random controls does not make any difference compared to only random controls. As Table 4 (and also Figure 1) indicates, both CR and RC have no impact on the probability of fare dodging compared to RR. This leads to our first result.

Result 1: Crackdowns fail reducing overall fare evasion.

We next consider the impact of pre-announcing audits. Model (3) of Table 4 reveals that participants are more likely to fraud in treatment CC_A and RR_A compared to the baseline (RR). The probability is 22.8% and 14.6% higher, respectively. This is also confirmed in Figure 1 (Panel B) where the average fraud rate is generally higher in RR_A compared to RR, and CC_A to CC. The reason, which is well captured by Figure 1, is that pre-announcement makes people fare dodging more when there is no audit. This leads to our second result:

Result 2: Pre-announcement of audits decreases their overall effectiveness.

We can investigate the effect of having longer crackdowns by looking at C_Long1 and C_Long2. The probability of committing a fraud is significantly higher

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
22 A crackdown ran from day 3 (33) until day 8 (38) but its effect operated from day 4 (34) until day 9 (39). In other words, the effect of a crackdown was one-day delayed. This is because subjects were not informed in advance of a crackdown. There is however an exception: in the CC_A treatment, the control was pre-announced and, therefore, the effect and execution of a crackdown coincided. For this treatment, crackdown days are 3-8 and 33-38. This is taken into account in Figure 3. in C_Long1 (17.1%) compared to RR while there is no significant difference between RR and C_Long2 (see Table 4). Figure 3 (Panel C) shows that fraud increases considerably after the introduction of an early longer crackdown (C_long1 treatment) and, to a lesser extent, before the introduction of a late longer crackdown (C_long2 treatment). This leads to our third result:

Result 3: Longer crackdowns are overall less effective if they occur in the early stage of the experiment.

To measure, other things being equal, the short-run effect of a crackdown (i.e. the immediate effect of a crackdown once it is introduced), we can look at the variable "Intensity Crackdown", that is the number of consecutive audits over time. We find that the probability to fraud, on average, drops by 5.8% in the immediate run for each consecutive day with an audit. This means that frequent consecutive audits discipline people in the short run. In Figure 2, we plot the marginal effect of each consecutive day of audit on the probability of not buying a ticket. We can see that the effect is not linear. The drop is sharp in the first days and it softens in the following. Fraud decreases by about 50% after 3/4 days, and it is almost eradicated after 9 days (only 1% or less of fraud). We can also look at the effect of being fined in the previous day.

Surprisingly, it has no additional impact on fraud. A possible explanation is that some people cheat more to recover from the loss while others cheat less because of the educative effect of the fine. The net effect is neutral.

The results of Table 4 also confirm our previous finding that actual fare-dodgers cheated more than actual non-fare-dodgers. In particular, self-reported fare-dodgers or non-ticket holders are much more likely to cheat than non-fare-dodgers (+39.7%).

The same applies to fare-dodgers recruited at the FCO (+29.9%). We also find that all the previous results (i.e. treatment effects and short-term impact of crackdowns) are even stronger among actual fare-dodgers (Columns 4-6). In contrast, there are no treatment effects among non-fare-dodgers. This provides important support to the external validity of our experiment and leads to our fourth result:

Result 4: Actual fare-dodgers fraud more than non-fare-dodgers and are more sensitive to our treatment manipulations.

On a final note, Table 4 shows that the risk attitude of subjects -in different domains (gains or losses) and information sets (uncertain or certain probabilities)does not explain behavior in our daily public transportation game. This suggests that the decision to act dishonestly is, in our setting, better explained by other factors, such as emotional, moral or social concerns, than simple cost-benefit considerations.

Relative efficiency in terms of payoffs

We now investigate the relative efficiency of the various audit policies from the point of view of the public transportation company by calculating the total revenue (paid tickets plus fines) that the company is able to collect. Figure 2 displays the total revenue for all our different treatments. Based on a Wilcoxon rank-sum test, we find no significant difference in revenue between treatments CR, RC, and RR (p > 0.1 for all possible comparisons). The revenue is instead significantly lower in treatments CC, C_Long1, C_Long2, CC_A, RR_A compared to RR (p = 0.020 for CC, and p < 0.001 for the other comparisons). This is in line with some of our previous findings and leads to our last result:

Result 5: Crackdowns do not increase the revenue of the law-enforcement institution.

[Figure 2 about here]

Conclusion

Our artefactual field experiment provides a comprehensive analysis of the relative efficiency and effectiveness of various crackdowns policies. The main finding is that crackdowns, alone, decrease overall effectiveness compared to random controls mostly because they induce a burst of fraud in the subsequent periods with no control.

Only when they are alternated with random controls or protracted for a longer time at the late stage of the game, 23 they achieve a level of overall compliance similar to a randomly distributed control policy. We also find that pre-announcing a control decreases overall compliance although it increases the effectiveness of a crackdown during its launch.

We believe all these results are very valuable for policy-makers who are contemplating which policy interventions to adopt against law-breaking behavior. In particular, our results suggest that under ambiguity in the domain of losses, systematic controls in a limited amount of time are, at best, as effective as random controls and potentially very inefficient in the long-run both in terms of achieved compliance and revenue for the law-enforcement institution.

One however should be careful in generalizing our results to any environment where crackdown policies may be relevant. Our study focuses on a specific field of application (i.e. public transportations), and look at a specific type of law violation (e.g. fare-dodging). It may be that crackdowns are very effective and efficient in other domains of application. This should be investigated in future studies.

Finally, although we try to be as comprehensive as possible by considering different and alternative policies of crackdown, there are still many grey areas which deserve future empirical investigation. For example, crackdowns may arise endogenously! (Dai, 2015a). Quoting Van de Weele (2012, p. 417), "enforcement strength is not exogenous, but determined by feedback effects between society and enforcers and social processes within the enforcement agencies themselves".

Crackdowns may also cause displacement effects, e.g. participants who are subjected to crackdowns will move to other areas during crackdown periods and thus decrease their efficiency. All these issues can be addressed in future studies.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
23 When the crackdown lasts longer and is localized towards the end of the game, subjects comply more during the period of no control as if they were expecting a control at any time.

Tables and figures

Figure 1 :

 1 Figure 1: Evolution of the average fraud rate by blocks of days over the sixty days

Figure 2 :

 2 Figure 2: Predictive margins of the fraud probability over consecutive days with audit

Figure 3 :

 3 Figure 3: Total revenue per ticket by treatment

Table 1 :

 1 Lotteries payoffsNote: The level of risk is represented by the standard deviation of the expected payoff.

Table 2 :

 2 Summary of the treatments

	Treatment	Days 1-30	Days 31-60
	Random-Random (RR)	Random audits	Random audits
	Crackdown-Crackdown (CC)	Crackdown (days 3-8)	Crackdown days (33-38)
	Crackdown-Random (CR)	Crackdown (days 3-8)	6 Random audits
	Random-Crackdown (RC)	Random audits	Crackdown (days 33-38)
	Early-Long-Crackdown (C_long1)	Crackdown (days 3-14)	No audit
	Late-Long-Crackdown (C_long2)	No audit	Crackdown (days 33-44)
	Crackdown-Crackdown with Pre-announcement (CC_A)	Crackdown (days 3-8)	Crackdown (days 33-38)
	Random-Random with Pre-announcement (RR_A)	Random audits	Random audits
	Note: The number of audits (12 in total) was constant across treatments.

Table 3 :

 3 Summary statistics on the fraud rate The "Test" column informs whether the fraud rate is different between fare-dodgers and non-fare-dodgers, according to a Wilcoxon rank-sum test. Standard deviations are shown in parenthesis.

		All	Fare-dodgers Non-fare-dodgers	Test
	RR (n = 38)	0.28 (0.45)	0.29 (0.45)	0.24 (0.43)	NS
	CC (n = 38)	0.36 (0.48)	0.44 (0.50)	0.14 (0.55)	***
	CR (n = 36)	0.25 (0.43)	0.34 (0.47)	0.11 (0.31)	**
	RC (n = 38)	0.29 (0.45)	0.35 (0.48)	0.06 (0.23)	***
	C_Long1 (n = 31)	0.38 (0.49)	0.44 (0.50)	0.30 (0.46)	NS
	C_Long2 (n = 36)	0.32 (0.47)	0.41 (0.49)	0.08 (0.26)	***
	CC_A (n = 31)	0.49 (0.50)	0.54 (0.50)	0.23 (0.42)	**
	RR_A (n = 31)	0.39 (0.49)	0.48 (0.50)	0.20 (0.40)	**
	Tot. (n = 279)	0.34 (0.47)	0.34 (0.47)	0.41 (0.49)	***

Notes: *** p<0.01, ** p<0.05, * p<0.1, NS p>0.1.

Table 4 :

 4 Random-effects probit model

			All Observations			Fare-dodgers only		Non-Fare-dodgers only
	Dependent variable: Fraud	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
	(1 if Fraud, 0 if not)	1 st Month	2 nd Month	All	1 st Month	2 nd Month	All	1 st Month	2 nd Month	All
	RR	Ref.	Ref.	Ref.	Ref.	Ref.	Ref.	Ref.	Ref.	Ref.
	CC	0.113	0.175**	0.142*	0.183*	0.282***	0.225**	0.006	0.007	0.014
		(0.080)	(0.080)	(0.079)	(0.103)	(0.103)	(0.103)	(0.046)	(0.052)	(0.038)
	CR	-0.025	0.022	-0.013	-0.005	0.078	0.021	-0.016	-0.020	-0.015
		(0.083)	(0.084)	(0.082)	(0.112)	(0.115)	(0.113)	(0.044)	(0.049)	(0.034)
	RC	0.034	0.042	0.040	0.096	0.123	0.110	-0.026	-0.028	-0.018
		(0.081)	(0.082)	(0.080)	(0.102)	(0.104)	(0.102)	(0.054)	(0.060)	(0.041)
	C_Long1	0.118	0.218**	0.171**	0.117	0.283**	0.204*	0.042	0.048	0.040
		(0.086)	(0.085)	(0.084)	(0.117)	(0.115)	(0.115)	(0.051)	(0.062)	(0.047)
	C_Long2	0.050	0.131	0.071	0.184*	0.261**	0.193*	-0.053	-0.022	-0.026
		(0.084)	(0.084)	(0.082)	(0.106)	(0.106)	(0.106)	(0.056)	(0.054)	(0.040)
	CC_A	0.186**	0.283***	0.228***	0.270***	0.410***	0.333***	0.046	0.050	0.039
		(0.083)	(0.082)	(0.082)	(0.104)	(0.101)	(0.102)	(0.065)	(0.073)	(0.054)
	RR_A	0.103	0.182**	0.146*	0.178	0.303***	0.239**	0.013	0.019	0.022
		(0.085)	(0.086)	(0.084)	(0.112)	(0.111)	(0.111)	(0.046)	(0.052)	(0.040)
	Intensity crackdown	-0.039***	-0.076***	-0.058***	-0.049***	-0.095***	-0.077***	-0.007**	-0.025*	-0.009*
		(0.004)	(0.005)	(0.004)	(0.005)	(0.006)	(0.004)	(0.004)	(0.013)	(0.005)
	Fined in the previous period	0.025	0.009	0.023	0.044	0.008	0.037*	-0.008	0.011	-0.003
		(0.021)	(0.023)	(0.015)	(0.029)	(0.032)	(0.021)	(0.012)	(0.016)	(0.007)

See, for example,Dai et al. (2015c) for a discussion on related studies.!

To strengthen the link of our experiment with the real world, we also frame the experimental setting in terms of the natural environment where these subjects take decisions about public transportation. This also facilitated the comprehension of the instructions for participants who possessed very different socio-economic and educational backgrounds.

[START_REF] Lando | The advantage of focusing law enforcement effort[END_REF] and[START_REF] Kleiman | The dynamics of deterrence[END_REF] are more interested on the implications of concentrating sanctions on a subset of violators rather than a period of time or geographical area.

The reason why we started the crackdown in day 3 and day 33 is that we did not want subjects to easily learn the occurrence of an audit.

If the audit probability was known, rational and risk-neutral agents should always choose to buy a ticket since the payoff would be higher than not to buy a ticket.

After having been punched, a ticket was valid for one hour. Hence, it was entirely legitimate and credible to compensate a ticket-holding subject with a new ticket for the time spent in the lab.

for research assistance. This research has been supported by a grant from Keolis, a grant of the French National Research Agency (ANR, FELIS Grant, ANR-14-CE28-0010-01), and funding from the European Commission (Marie Skłodowska-Curie Individual Fellowship, 661645 -IDEA -MSCA-IF-EF-ST). It was performed within the framework of the LABEX CORTEX (ANR-11-LABX-0042) of Université de Lyon, within the program Investissements d'Avenir (ANR-11-IDEX-007) operated by the French National Research Agency (ANR).!

Notes: The table reports marginal effects. These are calculated assuming that the random effects are zero. Standard


domain: spi qfin

text:
Andreas M Hein

Marija Jankovic

Romain Farel

Sam Lei

Bernard Yannou

Modeling Industrial Symbiosis Using Design Structure Matrices

Keywords: Industrial ecology, industrial symbiosis, eco-industrial park, systems architecture, DSM

Today, industry is under constant pressure to increase competitiveness and resource-efficiency. One possibility to cope with these challenges is industrial symbiosis. Industrial symbiosis is based on substituting a new resource by an undervalued resource such as waste. Thereby, industrial symbiosis reduces waste and saves resources. One of the practical challenges in developing industrial symbioses is the identification of symbiosis opportunities. In particular, the question how "new resourcesubstitute" combinations can be identified has not yet been addressed in the literature. This paper presents a modeling approach for industrial symbioses in industrial parks, based on design structure matrices (DSM), which intends to support the identification of substitution opportunities. The approach is applied to a sample industrial park. Combined with an optimization algorithm, the symbiosis model is used for identifying not only symbiosis opportunities but also the most attractive combination(s) of symbioses within the industrial park.

Introduction

An industrial symbiosis can be defined as "a flow of underutilised resource(s) (comprising substances and/or objects and/or energy), from an entity which would otherwise discard them, to another entity which uses them as a substitute for new resources." [START_REF] Deutz | Food for Thought: Seeking the Essence of Industrial Symbiosis[END_REF] An example for an industrial symbiosis is the use of waste water from a refinery as cooling water in a power plant for steam generation, depicted in Fig. 1. Without the symbiosis the power plant would use surface water from a lake. The refinery saves the cost of constructing waste water treatment facilities. The underutilized resource is therefore waste water. Without the symbiosis, it would be discarded and not further used. The power plant would use a new resource, which is the lake water. By establishing an industrial symbiosis, both symbiosis partners save cost and resources. Industrial symbioses play an important role in eco-industrial parks. An eco-industrial park is a set of businesses that share resources in order to increase profitability and reduce environmental impact [START_REF] Lowe | Eco-industrial park handbook for Asian developing countries[END_REF]. The most famous eco-industrial park is located at Kalundborg in Denmark. Over 40 different symbioses have reduced CO2 emission by about 8% and are saving three million tons of water per year [START_REF] Chertow | Quantifying economic and environmental benefits of co-located firms[END_REF][START_REF] Hodge | Quantifying potential profit from material recycling: A case study in brick manufacturing[END_REF][START_REF] Jacobsen | Industrial Symbiosis in Kalundborg, Denmark: A Quantitative Assessment of Economic and Environmental Aspects[END_REF][START_REF] Korhonen | Analysing the evolution of industrial ecosystems: Concepts and application[END_REF][START_REF] Sokka | Local systems, global impacts : Using life cycle assessment to analyse the potential and constraints of industrial symbioses[END_REF][START_REF] Tian | A formal program complexity model and its application[END_REF]. The waste water symbiosis in Fig. 1 is an existing symbiosis within the Kalundborg eco-industrial park. One of the challenges in defining an industrial symbiosis is to find options for with whom to form a symbiosis and what resource to exchange. Most of the existing literature focuses on how to optimize already identified industrial symbioses within an eco-industrial park or their process engineering aspects [START_REF] Cao | Applying agent-based modeling to the evolution of eco-industrial systems[END_REF][START_REF] Gu | Modeling and optimization of material/energy flow exchanges in an ecoindustrial park[END_REF][START_REF] Kim | Economic and environmental optimization of a multi-site utility network for an industrial complex[END_REF][START_REF] Maillé | Industrial By-Product Reuse and Synergy Optimization[END_REF][START_REF] Monteiro | Pareto optimization of an industrial ecosystem: Sustainability maximization[END_REF][START_REF] Schulze | Classification and development of mathematical models and simulation for industrial ecology[END_REF]. Existing approaches for identifying potential industrial symbioses have focused on the inputs and outputs of industrial plants [START_REF] Chertow | Industrial symbiosis: Literature and taxonomy[END_REF][START_REF] Schulze | Classification and development of mathematical models and simulation for industrial ecology[END_REF]. Inputs and outputs of the same type are matched. However, input / output matching is only capable of identifying obvious symbiosis opportunities where the type of input and output are identical, e.g. output: gypsum, input: gypsum. This approach would miss opportunities such as the aforementioned waste water symbiosis. In that case, fresh water is substituted by waste water. Finding proper substitutes is a non-trivial problem, as fresh water cannot be replaced by waste water in general but only under specific circumstances.

This paper addresses the non-trivial case of finding industrial symbiosis opportunities based on substitution by using design structure matrices (DSMs).

In the following, first, a terminology for designing industrial symbiosis is developed. Key concepts such as different concretization levels of symbioses and types of substitution are defined. The symbiosis DSM model is then based on these concepts. Finally, a methodology for identifying symbiosis opportunities and the optimal combination(s) of symbioses on a territory are presented.

Modeling Industrial Symbiosis with DSMs

DSMs have been used for numerous applications such as modeling the architecture of systems (componentcomponent DSM), processes within organizations (process DSM), relationships between parameters (parametric DSM), organizational capabilities (capability DSM), and component reuse (heritage DSM) [START_REF] Browning | Modeling impacts of process architecture on cost and schedule risk in product development[END_REF][START_REF] Browning | Applying the design structure matrix to system and integration problems: a review and new directions[END_REF][START_REF] Hein | How to Assess Heritage Systems in the Early Phases?[END_REF][START_REF] Hein | Towards a Capability Framework for Systems Architecting and Technology Strategy[END_REF][START_REF] Hein | World Ships-Architectures & Feasibility Revisited[END_REF][START_REF] Pektaş | Modelling detailed information flows in building design with the parameter-based design structure matrix[END_REF]. In this paper, DSMs are applied to identifying industrial symbiosis opportunities. What elements of a symbiosis need to be represented in a DSM? From a physical viewpoint, industrial symbioses include at least one material and energy flow. This physical viewpoint of industrial systems pertains to the concept of an "industrial ecosystem". In industrial ecosystems, industrial actors exchange material and energy flows, analogous to natural ecosystems [START_REF] Haberl | The energetic metabolism of societies part I: accounting concepts[END_REF]. The industrial ecosystem view extends the classic perspective of economics as a transfer of goods / money. It focuses on the physical basis of economic transactions such as resource consumption and waste creation. Leontief has Andreas M. Hein, Marija Jankovic, Romain Farel, I Sam Lei, Bernard Yannou DSM 2015 developed matrix-based model for industrial activities and has proposed a model that maps the classical economic perspective to the industrial eco-system perspective [START_REF] Leontief | Input-Output Economics[END_REF][START_REF] Leontief | Environmental repercussions and the economic structure: an input-output approach[END_REF]. In this paper, we limit the model to the material and energy flows that are associated with symbiosis opportunities and not material and energy flows in general.

2.1

Modeling Industrial Symbiosis For modeling industrial symbioses with DSMs, we need to develop a terminology for describing an industrial symbiosis [START_REF] Hein | A Conceptual Framework for Eco-Industrial Parks[END_REF]. We use the following statements as a baseline:

-An industrial symbiosis includes at least one material / energy flow.

-The material / energy flow is an underutilized resource supplied by one symbiosis partner. This symbiosis partner is called "supplier". -The symbiosis partner that uses the resource as a substitute is called "receiver".

-Symbiosis partners can have different roles in different symbioses. A partner can be a receiver in symbiosis A and a supplier in symbiosis B. -The material / energy flow is transferred from the supplier to the receiver. In addition, it may be converted. -A set of industrial symbioses within an industrial park is called a symbiosis network. We use the following limitations for facilitating the development of an initial DSM model:

-Symbioses with a single material / energy flow.

-Flows are only transferred but not transformed. After having defined the terminology and limitations, steps in defining industrial symbioses are presented next.

2.2

Symbiosis concretization stages For identifying industrial symbioses systematically, different levels of concretization are defined, analogous to design process steps in classic product development [START_REF] Otto | Product Design: Techniques In Reverse Engineering And New Product Development Author[END_REF][START_REF] Pahl | Engineering design: a systematic approach[END_REF]. Fig. 3 provides an overview of the concretization levels.

Fig. 3: Levels of concretization of industrial symbiosis

Potential symbiosis

A potential symbiosis exists when there is a potential supplier that is able to offer an underutilized resource and there is another potential receiver that has a demand for the resource as a substitute for a new resource.

DSM 2015

At this point, it is necessary to clarify the notion of "substitute". In its original sense, a substitute is a replacement for something. The replacement is not necessarily identical with the thing being replaced. To account for this distinction, we propose the following types of substitutes:

-Identical: A substitute is identical if it is indistinguishable from the original resource in its composition and can be used as an input for the same function(s), e.g. a boiler has the function to heat water and can use natural gas as an input.

The existing supplier for natural gas can be substituted by natural gas from a different supplier. Fig. 3 shows an example where steam is substituted by steam. -Functional substitute: The substitute differs from the original resource in its composition but can be used as an input to the same function. For example, methane from biomass may substitute natural gas for producing steam in a boiler (function: produce steam). Due to the difference in composition, there might be compatibility issues with using the substitute such as lower performance or degradation of equipment.

Note that substitution is not limited to a plant's inputs and outputs. Only taking inputs and outputs into consideration misses opportunities for symbioses that are based on energy / material flows within a plant. For example, steam is generated within a plant by a boiler. The boiler is fueled by natural gas. Two substitutions are possible. First, the natural gas (an input to the plant) can be substituted, e.g. by methane. This symbiosis opportunity could be detected by looking at the input of the plant. Second, external steam can be used, replacing the boiler. This symbiosis can only be detected when information about the generation of steam within the plant is available.

Functional symbiosis

A functional symbiosis is a symbiosis where the infrastructure for transferring / converting / storing the resource is defined on a functional level, i.e. the inputs and outputs and the transformation are specified. To use a standardized way to describe functions, the "functional basis" is used, which is presented in [START_REF] Hirtz | A functional basis for engineering design: reconciling and evolving previous efforts[END_REF][START_REF] Stone | Development of a functional basis for design[END_REF]. Fig. 3 shows an example where steam is transmitted by the symbiosis infrastructure. As mentioned before, this paper only deals with the case of transferring a resource, which includes the transmission of energy and the transportation of material.

Technological symbiosis

The technological symbiosis is a symbiosis where the infrastructure for transferring / converting / storing the resource is defined at a technological level. This means that the working principles of the technology and fundamental design data such as length of a pipeline are defined, allowing for a high-level economic feasibility analysis [START_REF] Pahl | Engineering design: a systematic approach[END_REF]. Fig. 3 shows an example where a pipeline is used for transmitting steam.

Andreas M. Hein, Marija Jankovic, Romain Farel, I Sam Lei, Bernard Yannou DSM 2015

Multigraphs with ports and DSM

The formal representation of industrial symbiosis is firmly grounded in classic graph theory and the more recent concept of multigraphs with ports [START_REF] Andrei | A rewriting calculus for multigraphs with ports[END_REF][START_REF] Andrei | A Rewriting Calculus for Graphs: Applications to Biology and Autonomous Systems[END_REF][START_REF] Bondy | Graph theory with applications[END_REF][START_REF] Bretto | Eléments de théorie des graphes[END_REF]. The symbiosis DSM is a view created from this formal representation. A directed multigraph with ports extends a directed multigraph by the concept of "ports". The concept was introduced in a formal manner by [START_REF] Andrei | A rewriting calculus for multigraphs with ports[END_REF][START_REF] Andrei | A Rewriting Calculus for Graphs: Applications to Biology and Autonomous Systems[END_REF]. Ports are explicit connection points that are associated with nodes. Edges attach to ports. Ports can be used to represent interfaces. Interfaces are relevant for biological and artificial systems. In [START_REF] Andrei | A Rewriting Calculus for Graphs: Applications to Biology and Autonomous Systems[END_REF], ports were used for modeling attachment points for proteins and interfaces between elements of an autonomic system. An example for a directed multigraph with ports is shown in [START_REF] Andrei | A rewriting calculus for multigraphs with ports[END_REF] For modeling industrial symbioses with multigraphs with ports, the following elements are added to the original definition:

-A port type can be assigned multiple times to a node, e.g. multiple steam ports. -Labels "supply" and "demand" can be assigned to each port, abbreviated as "s" and "d". A supply port can only have outgoing edges and a receiver port only ingoing edges. Grounded in formal graph theory, the different DSMs are created from multigraphs with ports where the rows in the DSM represent supply ports and the columns receiver ports.

2.4

Modeling symbioses as directed multigraphs with ports Table 1 shows the mapping between the elements of a multigraph with ports and different symbiosis concretization levels. Nodes represent industrial actors such as industrial plants, urban areas, and agricultural businesses. Ports can represent a potential resource supply a and a resource demand b. At this level, supply and demand does not need to be a physical in-or output of an industrial actor. By contrast, for the functional and technological symbiosis, we assume that there is a physical input or output port of the actor that allows for a transfer of the resource, e.g. sulfur entering into the actor. In this case, b is no longer the resource substituted but the resource a after the transfer. DSM 2015

Application example

The modeling approach is applied to a sample industrial park, based on an existing industrial park in France. The case consists of four industrial plants: a refinery, a toxic waste incinerator, a pharmaceutical plant, and a biomass incinerator. The supply and demand values for the plants have been modified but resemble typical values for these types of plants. Do industrial symbiosis opportunities exist in this industrial park? If yes, which combination of symbioses is most attractive from an economic and environmental point of view? Commonly, detailed data for plant inputs, outputs, and internal processes are confidential. Hence, the analysis has to start with a priori assumptions and estimates.

A schematic aerial view of the industrial park is shown in Fig. 6.

The following steps are performed in order to identify potential symbioses and to find the best combination of symbioses: 1. Create potential symbiosis DSM and identify substitution opportunities. 2. Solve the supply / demand allocation problem by using an optimization algorithm.

DSM 2015 Fig. 6: Schematic aerial view of a fictive industrial park Fig. 7 shows a section of the potential symbiosis DSM for the industrial park. The DSM was created by listing all in-and outputs of plants, major intermediate resource flows within the plants, and substitutes for them. It can be seen that there is a match for steam from the biomass incinerator to the pharmaceutical plant and organic waste from the pharmaceutical plant to the biomass incinerator. Note that the addition "substitute natural gas" indicates that the demand would substitute for the input "natural gas". It is important to define possible substitutes for each plant type, as what can be substituted by what often differs from plant to plant. Each of the resource supplies and resource demands has a quantity. The amount of supply matching a demand cannot exceed the available supply. Furthermore, the amount of supply matching a demand cannot exceed the total demand. These two constraints can be formulated as

𝑆 𝑖 ≥ ∑ 𝑠 𝑖𝑗 𝑛 𝑗=1
where 𝑠 𝑖𝑗 is a supply i that meets a demand j. The sum of 𝑠 𝑖𝑗 cannot exceed the total available supply 𝑆 𝑖 .

DSM 2015

𝐷 𝑗 ≥ ∑ 𝑐 𝑖 𝑠 𝑖𝑗 𝑚 𝑖=1
Furthermore, the sum of supplies 𝑠 𝑖𝑗 for a demand 𝐷 𝑗 has to be equal or less than the demand. 𝑐 𝑖 is a conversion factor for treating up-and downstream substitutes. For example, if the demand is steam, either steam is supplied directly, in which case 𝑐 𝑖 would be 1, or indirectly, e.g. by burning methane in a boiler. For methane, 𝑐 𝑖 would be the ratio of a unit of steam produced per unit of methane. By using conversion factors, upstream flows can be converted into downstream flows. Here, we have a simple case with only one technology option for transmitting energy or transporting material. The distances between plants are estimated by calculating a distance matrix from the plants' coordinates. Note that these are only examples for objective functions and we can easily imagine alternatives to these given. For example, we could separate between energy substituted and material substituted. Another way would be to calculate the equivalent of reduction in CO2 emission. The supply / demand allocation problem in this case can be formulated as the multiobjective optimization problem with the objective functions The problem is solved by using a multi-objective genetic algorithm (MOGA). MOGA is chosen, as it is scalable and leaves the possibility open for using non-linear objective functions and constraints. Non-linearity may come into play with economy-of-scale effects and discounts on resource flows. Table 2 shows the properties of a sample Paretooptimal symbiosis network. Note that it would not have been possible to detect the steam symbioses with an input / output matching alone as steam is generating within the pharmaceutical plant. The objective function vector for this symbiosis network is depicted in Table 3. The resource savings are considerable. The main resource saved is steam, which is a means for transporting energy. It can be seen that the capital investments could be paid back by the net profit after one to two years. Note that for a more elaborate economic model, net present value (NPV) should be used for discounting future cash flows.

Conclusions

This paper presents a modeling approach for industrial symbioses, based on DSMs in order to facilitate the identification of feasible symbioses. The modeling approach extends the existing inputoutput matching approaches by including different types of resource substitutions. It is demonstrated that the modeling approach can be used for identifying potential symbioses and searching for optimal symbiosis networks. It is furthermore demonstrated that the approach is capable of finding symbiosis opportunities that would not be found by an inputoutput matching approach alone. Future work aims at including symbiosis infrastructure technologies that are able to convert resources. Taking conversion into account would open up the possibility for finding further symbiosis opportunities. Finally, the ultimate objective of this work is to support the creation of industrial symbioses in reality, thereby increasing the competitiveness and sustainability of industry.

Fig. 1 :

 1 Fig. 1: Waste water-based symbiosis at Kalundborg

  Fig 4. The nodes and ports have "types" associated with them such as A, B, and C for nodes and a, b, c, d, and e for ports. 1, 2, 3, 4 are unique identifiers for the nodes. Multiple edges can attach to a port.

Fig. 4 :

 4 Fig.4: Sample directed multigraph with ports from[START_REF] Andrei | A rewriting calculus for multigraphs with ports[END_REF]

Fig. 5 Fig. 5 :

 55 Fig.5depicts an example symbiosis DSM with two potential symbioses. The edge (supply a, demand a) is a trivial match between a supply of resource a and a demand for a. A functional symbiosis opportunity (supply b, demand d) exists between supply b and demand d. The matrix diagonal is colored in grey in order to indicate that supply and demand for the same plant cannot be matched.

Fig. 7 :

 7 Fig.7: Part of the potential symbiosis DSM for the fictive industrial park

Table 1 :

 1 Multigraph with ports for modeling different symbiosis concretization levels

	Multigraph with	Potential symbiosis Functional			Technological
	port element			symbiosis			symbiosis
	Node	Industrial actor	Industrial actor		Industrial actor
	Port	Potential	supply	Physical output a or	Physical output a or
		resource type a,	input b of industrial	input b of industrial
		demand	resource	actor			actor
		type b
	Edge	Supply	resource	Output	a	is	Output	a	is
		type a can substitute	transferred to input b	transferred to input b
		demanded resource	by	function	by technology x
		type b		"transfer"

  Conversion factors allow for calculating the total amount of new resources that are substituted. Three criteria are used for evaluating the symbiosis networks: -Maximize the quantity of substituted new resources 𝑠 𝑖𝑗 . -Maximize net profit, simplified as revenue 𝑟 𝑖𝑗𝑘 minus operating cost 𝑜 𝑖𝑗 for a match 𝑠 𝑖𝑗 . -Minimize capital investments 𝐶 𝑖𝑗 for a technology to transfer 𝑠 𝑖𝑗 . (Pipeline for transmitting steam: 1M$/km; $100,000 per truck transporting 20t of organic waste)

Table 2 :

 2 Set of symbioses for optimal symbiosis network

	Supplier -receiver	Resource	Quantity [t/a]
	Toxic waste incinerator -refinery	Steam	200,000
	Pharmaceutical plant -biomass incinerator	Organic waste 50,000
	Biomass incinerator -refinery	Steam	280,000

Table 3 :

 3 Values for the objective function for the optimal symbiosis network Note that in reality each individual symbiosis has to be economically feasible. This condition can be represented by additional constraints, for example, a positive NPV for each symbiosis.

	Objective functions	Values for a sample Pareto-optimal
		symbiosis network
	New resources 𝑠 𝑖𝑗 substituted (steam, biomass) 530,000 t/a
	Net profit 𝑟 𝑖𝑗 -𝑜 𝑖𝑗	2.5M$
	Capital investments 𝐶 𝑖𝑗	4.5M$

DSM 2015

Acknowledgements

The authors gratefully acknowledge the generous support by the following French and international industrial actors: Air Liquide, TOTAL, and EDF R&D.