Francesca Bassi
email: francesca.bassi@irt-systemx.fr

Hatem Ibn Khedher
email: hatem.ibn-khedher@parisdescartes.fr

HARQ-aware allocation of computing resources in C-RAN

The principal tenet of C-RAN is the softwarization of the base-band signal processing, which enables the sharing of computing resources among multiple radio heads. When the aggregate demand exceeds the processing capacity, a fraction of the radio packets is lost at PHY layer. Traditional computing resource allocation policies aim to minimize the packet loss rate.

Dropping a PHY packet triggers a retransmission, unless the lost packet corresponds to the last available HARQ round, in which case the entirety of the radio resources spent on the multiple transmissions go to waste. This suggests that allocating computing resource accounting also for the HARQ transmission history may make a more efficient use of the bandwidth.

We consider a simplified LTE uplink setting, and we measure the performance at the lower MAC layer (accuracy, goodput and average delay). We first compare the PHY-layer loss rate minimization and the cross-layer approaches using an ILP formulation. The cross-layer approach brings a tangible improvement, especially in accuracy. This suggests, for future work, that joint radio and computing resource allocation may further enhance spectral efficiency. We finally propose a probabilistic algorithm amenable to real-time operation which allows to mix strategies via parameter tuning, and we use it to explore the region of achievable goodput/accuracy trade-offs.

I. INTRODUCTION

Cloud-RAN or C-RAN [1], [START_REF] Wang | C-RAN: The Road Towards Green RAN[END_REF] is a radio access paradigm for mobile networks capable of responding to the economic challenges of network densification [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF]. In the traditional mobile architecture users access the network by connecting to a radio base station. The base station can be functionnally separated into radio functions, for the transmission of the analog radio-frequency waveform, and base-band functions, for the digital processing before radio-frequency conversion. The enabler of C-RAN is the softwarization of the baseband functions, which allows to split the base station into a Radio Head (RH) and a Base-Band Unit (BBU). As the base station in the traditional architecture, the RH needs to be geographically deployed to provide radio coverage, while the BBU can now run remotely, in a data center that simoultaneously serves a multitude of RHs.

A big challenge for C-RAN is the respect of the latency constraints imposed by the communication protocol stack [4]. In LTE, for instance, the HARQ protocol triggers the retransmission of a radio packet if the correct reception of the message has not been acknowledged within 8 milliseconds. This imposes a hard deadline of 3 milliseconds to complete the base-band processing of a received subframe, accounting for both the propagation time in the fronthaul and the processing time in the BBU. Latency, bandwith and cost issues of the fronthaul are the object of many studies (see [START_REF] Alimi | Toward an efficient C-RAN optical fronthaul for the future networks: a tutorial on technologies, requirements, challenges, and solutions[END_REF] and references therein). In order to solve some of these issues, alternative functional splits have been proposed [START_REF] Peng | Fronthaul-constrained cloud radio access networks: insights and challenges[END_REF], where also a portion of the base-band processing takes place in the distributed unit, along with the radio functions. In this work we stick to the standard functional split considered in [1], [START_REF] Wang | C-RAN: The Road Towards Green RAN[END_REF], with remote RHs and central BBUs.

The policy of allocation of the shared computing resources has an impact in many respects. Some works investigate strategies to optimize the power consumption [START_REF] Qian | Baseband processing units virtualization for cloud radio access networks[END_REF]; some consider demand anticipation and resource provision [START_REF] Pompili | Elastic resource utilization framework for high capacity and energy efficiency in cloud RAN[END_REF]; some try to to reduce the overall processing time exploiting parallelization [START_REF] Garikipati | RT-OPEX: Flexible scheduling for Cloud-RAN processing[END_REF], [START_REF] Rodriguez | Cloud-RAN modeling based on parallel processing[END_REF]; some focus on the orchestration of the virtualized functions [START_REF] Matoussi | A User Centric Virtual Network Function Orchestration for Agile 5G Cloud-RAN[END_REF]. The problem is especially interesting in the uplink, where the central BBU is in charge of channel decoding. Since each user transmits with a different Modulation Coding Scheme (MCS), and since the processing times for different MCSs vary widely [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF], it may be difficult to anticipate the instantaneous demand and allocate enough computing resources, so that packets may not get processed within the required deadline. We model these events as packet losses at PHY layer. The computing resource allocation algorithms found in the literature generally aim to minimize the packet loss rate [START_REF] Garikipati | RT-OPEX: Flexible scheduling for Cloud-RAN processing[END_REF], [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF], which is a very natural choice.

A packet loss triggers a negative acknowledgement in the HARQ protocol at MAC layer. Hence, if the lost packet corresponds to the last allowed transmission, the message will never be correctly received, and the system squandered all the radio resources spent on it with the last and previous transmissions. Starting from this simple observation, we explore whether a cross-layer policy for allocating the computing resources may use the bandwidth more efficiently. We still assume that radio scheduling and computing resource allocation are separate processes, but we account in the latter for the retransmission age of the message, i.e., for the HARQ round.

We consider a simplified version of the LTE uplink, where each subframe is occupied by a single user, and we measure the performance through the Bit Error Rate (BER), the average delay and the Goodput at MAC layer. The Goodput is defined as the (long-term) average number of correctly received bits per unit of time [START_REF] Wu | Coding versus ARQ in fading channels: How reliable should the PHY be?[END_REF]. The system and simulations setups are described in detail in Sections II and III, respectively. The allocation policy that minimizes the PHY packet losses is formulated as an Integer Linear Program [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF] in Section IV, where we turn it in a cross-layer policy by incorporating the HARQ retransmission age of the message in the objective function. This achieves a consistent improvement in the BER, for the same Goodput, at the expense of the average delay. Resource allocation via ILP is not practically viable because of its complexity. In Section V we propose a probabilistic algorithm, which is amenable to real-time operation and allows to implement the same strategies of the ILP formulation by appropriately tuning its three parameters, incurring a modest performance degradation. The low complexity of the probabilistic algorithm allows to exhaustively explore the space of the parameters, in Section V-A. This corresponds to probing all mixed strategies, which is unfeasible with the ILP formulation. It is confirmed that the strategy providing the the most effective Goodput/accuracy trade-off consists in allocating computing resources in priority to subframes with high information content and old retransmission age.

II. SYSTEM SETUP AND PROBLEM DEFINITION

We consider a C-RAN architecture [1], [START_REF] Wang | C-RAN: The Road Towards Green RAN[END_REF] and we focus on the uplink from multiple RHs towards a centralized BBU. We assume that the radio scheduling, the PHY layer and the lower MAC layer work as in LTE. Let N be the set of the RHs, which we assume operate in the 20 MHz bandwidth, so that the number of physical resource blocks per subframe is 100 [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF], [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF], for all RH. We assume that each subframe carries data of a single user and uses only one MCS.

In LTE the PHY subframes originate from the transmission of MAC messages via a stop-and-wait HARQ process [START_REF] Larmo | The LTE link-layer design[END_REF]. We consider synchronous HARQ, and each RH treats P = 8 parallel messages in a pre-defined order. The maximum number of transmissions per message is T max = 4. Each subframe i is tagged by r i ∈ {1, 2, ..., T max }, which indicates which HARQ round the subframe represents. Since the HARQ is synchronous the tag is known at the BBU and does not need to be signalled explicitly. We assume non-adaptive HARQ, so that the MCS stays constant across HARQ retransmissions. To allow HARQ control messages to be received on time each subframe must be processed by the BBU within d = 2 TTIs from reception, otherwise it is lost.

The BBU pool consists of the set C of CPU cores. Each core in C has the same execution speed and can process at most one subframe at a time. Processing is not parallelized and a subframe fully occupies a core for the entire duration of its processing. The MCS of subframe i determines its processing time t i , as well as its information content of b i information bytes [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF]. Each RH presents a subframe to the BBU each TTI, which in LTE has a duration of 1 ms. For simplicity, we assume that K = |C| d is an integer value. At each TTI the resource allocation problem consists in reserving, for each of the |N | most recently received subframes, the appropriate amount of time in one of the K available CPU cores, so that the subframe is processed within the deadline d. At each TTI, if the system is in moderate load the expected value of the demand of processing time is smaller or equal to the available processing time, i.e. i∈N E[t i ] ≤ dK. The expected number of PHY subframes losses in the TTI is zero. Otherwise, the system is in overload, and losses of PHY subframes are expected. Since in our setup all the RHs present a subframe at each TTI, all the subsets K experience the same level of load (moderate or overload), depending on the value |N |. So the resource allocation can be performed in independent subgroups of K cores each, without loss of optimality.

We want to investigate the impact of the computing resource allocation policy on the metrics observed at MAC layer. We consider the Bit Error Rate (BER), defined as the number of incorrectly received information bits over the total number of transmitted information bits (an information bit is considered incorrectly received if the subframe it belongs to has not been ACKed after T max transmissions); the Goodput, defined as the average number of information bits correctly received per TTI; the average delay, defined as the average number of transmissions for successfully received MAC logical unit. At PHY layer, we consider the Subframe Rejection Rate (SRR), defined as the number of lost (because of the resource allocation policy) subframes over the total number of subframes demanding processing; and the Bit Rejection Rate (BRR), defined as the number of lost information information bits over the total number of information bits demanding processing.

III. SIMULATION SETUP AND PARAMETER CHOICE

The performance of the considered computing resource allocation strategies are obtained using Monte Carlo simulations, whose setup is as follows. Each of the |N | RHs manages a synchronous HARQ process with P = 8 parallel data streams. All transmissions of the same message use the same MCS (see Section III-A on MCS sampling). At each TTI each RH presents a subframe to the BBU, and the computing resource allocation algorithm specifies the set of subframes which get processed. The algorithm may use information about retransmission tags (known because of synchronous HARQ), information content (dependent on MCS) and processing time (dependent on MCS) of the subframes (see Section III-B). Subframes rejected by the BBU trigger NACKs in the HARQ process. Subframes accepted by the BBU might be successfully (triggering ACK) or unsuccessfully (triggering NACK) decoded. The decoding outcome is sampled using precomputed probabilities dependent on the retransmission tag and MCS of the subframe (see Section III-C). The maximum number of HARQ transmissions is T max = 4. The simulation lasts 500 TTI, and the performance is evaluated in terms of BER, Goodput, average delay and SRR, BRR. The simulations use the GLPK optimization library to solve the ILP.

A. MCS sampling

When a MAC message is generated it is associated with an MCS, which is constant for all HARQ transmissions. For MCS sampling we use, as in [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF], an empirical distribution evaluated from the data set in [START_REF] Trinh | Analysis and modeling of mobile traffic using real traces[END_REF]. The data set [START_REF] Trinh | Analysis and modeling of mobile traffic using real traces[END_REF] records real traffic in 4 mobile cells and reports the MCS occurrence. The resulting empirical distribution has a median MCS equal to 8, and a mean MCS equal to 8.62. The sampled MCS is between 4 and 14 with probability 0.9.

B. Processing time and information content

Both the information content b i in information bits and the processing time t i of subframe i can be determined by its MCS. As the MCS increases, both t i and b i increase. In this work we use the numerical values found in [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF].

C. Decoding failure probabilities

In order to sample the decoding outcome (ACK or NACK) of processed subframes, the Monte Carlo simulation needs π k , defined as be the probability that a message is NACKed after the k-th transmission. To estimate these probabilities we make use of a data set obtained by running the LTE PHY layer on Open Air Interface (OAI). The experiment concerns the transmission in uplink (from User Equipment to RH) of a MAC message. The PHY subframe is composed by 100 resource blocks. The MCS of the subframe and the SINR are constant across HARQ retransmissions. The receiver performs Chase Combining and the maximum number of transmissions is T max = 4. The experiment is repeated 500 times for any configuration of (SINR, MCS), with MCS ∈ {0, 2, 4, ..., 26} and SINR ∈ [-5, 18] dB. The data set records the average Block Error Rate (BLER k ) after transmission k, k ∈ {1, 2, ..., T max }. BLER k is the proportion of experiments where the MAC message is in NACK after k transmissions have elapsed. An estimate π k is obtained dividing the number of times NACK happened after the k-th transmission by the total number of times a unit has been transmitted at the k-th round. This is calculated from the dataset as π 1 = BLER 1 for k = 1, and for k > 1 as π k = BLER k BLER k-1 . From the dataset we hence get the estimates π k (MCS, SINR) for k ∈ {1, ..., T max }. In LTE the radio scheduler allocates the radio resources (radio resource blocks, power and MCS) such that BLER 1 ≤ 0.1. Using this information, we select for each MCS the SINR which provides BLER 1 ≤ 0.1. We then obtain estimates π k (MCS) parametrized only by the MCS.

IV. RESOURCE ALLOCATION AS AN OPTIMIZATION

PROBLEM

Given the K available cores and the set of instantaneous processing demands, the resource allocation problem consists in identifying the subset of subframes which will be processed and their execution cores. The problem can be formulated as an Integer Linear Program whose solution (evaluated each TTI) is the computing resource allocation policy. This formulation has already been explored in [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF], where the optimization problem is expressed as follows:

maximize i∈N c∈K x c i (1) subject to x c i ∈ {0, 1}, ∀i ∈ N , ∀c ∈ K, (2)
c∈K x c i ≤ 1, ∀i ∈ N , (3)
i∈N t i x c i ≤ d, ∀c ∈ K. (4)
Constraint (2) says that x c i is a binary quantity. The value x c i = 1 means that subframe i gets assigned to core c for processing. Constraint (3) imposes that each subframe is processed at most once, and constraint (4) imposes that the processing of all the subframes allocated to the same core is completed within the deadline d. The objective (1) is to schedule a maximum number of subframes. In case of moderate load all requests get satisfied. In case of overload subframes associated with a smaller t i get processed with higher priority, which maximizes the number of subframes which get processed. Since t i increases with the MCS [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF], subframes with high MCS have a bigger risk of being lost.

In [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF] it is also considered an objective function accounting for the information content of the subframe. The constraints (2), ( 3), (4) remain the same, while the objective function is

maximize i∈N c∈K x c i b i , (5)
where b i is the information content in bytes of subframe i. The allocation strategy corresponding to the ILP with objective function [START_REF] Alimi | Toward an efficient C-RAN optical fronthaul for the future networks: a tutorial on technologies, requirements, challenges, and solutions[END_REF] gives higher priority to subframes with high information content (high MCS). Since these are also the most demanding in processing time, this strategy must find the best trade-off between information content and execution time.

We propose a cross-layer resource allocation policy via ILP formulation, with constraints (2), ( 3), ( 4) and the following objective function:

maximize i∈N c∈K x c i + α r i T max + β b i B , (6)
where , α and β are parameters taking values in {0, 1}. The parameter B in ( 6) is the maximum information content of a subframe, which corresponds to the information content of a subframe with maximum MCS [START_REF] Khedher | Processing time evaluation and prediction in Cloud-RAN[END_REF]. The quantity b i /B is hence the normalized information content of subframe i. Similarly, r i /T max indicates the normalized transmission age of subframe i. Notice that for ( , α, β) = (1, 0, 0) the objective function ( 6) becomes (1); for ( , α, β) = (0, 0, 1) the objective function ( 6) becomes equivalent to [START_REF] Alimi | Toward an efficient C-RAN optical fronthaul for the future networks: a tutorial on technologies, requirements, challenges, and solutions[END_REF]. When ( , α, β) = (0, 1, 0) we obtain a scheduling policy where older subframes in the HARQ protocol have higher priority. We also consider ( , α, β) = (0, 1, 1), strategy where the highest priority is given to subframes with big information content and also old in the HARQ process. The solid lines in Figures 1 and2 present the metrics, at PHY layer and MAC layer respectively, of the resource allocation algorithm via ILP formulation (6), ( 2), (3), (4). In this setting K = 1. The legend indicates the vector ( , α, β) used to define the objective function [START_REF] Peng | Fronthaul-constrained cloud radio access networks: insights and challenges[END_REF]. All metrics are shown as a function of the number of connected RHs. As it can be seen in Figure 1 from the average CPU load (expressed as the fraction of the scheduled computation resources), when more than 25 RHs are connected the system is in overload. The SRR in Figure 1 shows that all considered strategies provide similar results on the number of processed PHY subframes. As expected ( , α, β) = (1, 0, 0) (yellow curve) gives the best SRR, which is however only less than 1 dB away of the worst case. This suggests that PHY losses are not a very good metric to guide the choice of the allocation policy, since there is not a strong reason to prefer a policy over the others based on SRR only. On the other hand, the BRR in Figure 1 shows that the ILP for ( , α, β) = (0, 0, 1) (red curve), provides the best BRR [START_REF] Khedher | Real Traffic-Aware Scheduling of Computing Resources in Cloud-RAN[END_REF], and that the improvement over to the worst case (yellow curve) is substantial (over 5 dB). The intuition that optimizing the number of processed information bits a PHY layer is a good proxy for optimizing the Goodput at MAC layer is confirmed by the plot of the Goodput in Figure 2, where we can see that the red curve is the best performance. Figure 2 shows the MAC layer metrics, on which we evaluate, in this work, the performance of the allocation policy. Inspecting the BER, we can see that maximizing the number of processed subframes (yellow curve) and even maximizing the number of processed information bits (red curve) are suboptimal with respect to ILP for ( , α, β) = (0, 1, 0) (blue curve), which gives priority to older subframes. This confirms that considering also the retransmission age brings the performance improvement in accuracy we hoped for. This comes at the cost of a degradation of the average delay, which however does not impact too dramatically the Goodput, as visible in Figure 2. Finally, notice that optimizing the number of processed subframes (yellow curve) gives, albeit achieving the best average delay, the worst Goodput among the considered strategies, due to the very poor accuracy, as seen in the plots in Figure 2.

The two good strategies that emerged so far can be combined. Maximizing the processed information bits while giving priority to older subframes, as done in ILP with ( , α, β) = (0, 1, 1) (purple curve), further increases the gain in terms of BER of the (0, 0, 1) strategy (blue curve), without degrading in a very significant way the average delay and keeping the Goodput close to the blue curve. This strategy globally achieves a good trade-off between accuracy and Goodput.

V. THE PROBABILISTIC ALGORITHM

Computing resource allocation via ILP formulation is not a viable solution for real systems because it is a computationally complex problem which needs to be solved very frequently (at each TTI). In this section we propose an alternative algorithm, which draws inspiration from the results of Section IV. The algorithm consists in repeatedly sampling elements from the set of received subframes and scheduling them for processing as long as computing resources are still available. More precisely, let S be the set of subframes demanding processing resources at a given TTI, and let T K be the processing time available in the BBU. The algorithm works in rounds. At the beginning of each round, the subframe i is sampled with uniform distribution from S. If t i ≤ T K , i.e. enough processing resources are still available, subframe i gets scheduled with probability

ϕ i = 1 ( + α + β) + α r i T max + β b i B . (7)
If subframe i is scheduled, T K is diminished by t i and subframe i is removed from S. If i is not scheduled the available computing resources stay unchanged and the subframe is not removed from S. The algorithm repeats rounds until the remaining resources in T K are not sufficient to process the fastest element still in S, or until no subframe has been scheduled in the last L consecutive samplings. The expected number ν of rounds to complete the algorithm is upper bounded by

ν ≤ T K min i {t i } 1 min i {ϕ i } + L. (8)
The computational cost of the probabilistic algorithm can be hence approximated by the cost of performing ν random samplings.

The parameters ∈ {0, 1}, α ∈ {0, 1} and β ∈ {0, 1} in (7) play the same role as in the ILP objective function [START_REF] Peng | Fronthaul-constrained cloud radio access networks: insights and challenges[END_REF]. For ( , α, β) = (1, 0, 0) the probabilistic algorithm samples subframes from S and allocates them with probability 1 until the computing resources are occupied. For ( , α, β) = (0, 0, 1) the higher is the information content of the sampled subframe, the higher is the probability that it gets scheduled. Similarly, for ( , α, β) = (0, 1, 0) the older is the HARQ transmission history of the sampled subframe, the higher is the probability that it gets scheduled. For ( , α, β) = (0, 1, 1) the probability of getting scheduled increases both with the information content and with the retransmission age.

The performance of the probabilistic algorithm is indicated by the dotted curves in Figures 1 and2. The curves keep the same color code of their ILP counterparts. As expected, for the SRR the performance of the probabilistic algorithm for (1, 0, 0) (yellow curves) is suboptimal with respect to the performance of the ILP algorithm; similarly, the ILP algorithm outperforms the probabilistic algorithm for (0, 0, 1) (red curves) for the BRR. However we observe that in both cases the probabilistic algorithm performs better with respect to the BER observed at MAC layer, as visible in Figure 2. For the (0, 1, 0) strategy, the ILP and probabilistic algorithms achieve comparable performance in terms of average delay and Goodput, even if the BER is mildly degraded for the probabilistic algorithm. Combining strategies, as in ( , α, β) = (0, 1, 1) does not provide, with the probabilistic algorithm, the same gain over the (0, 1, 0) strategy as in the ILP formulation, but still remains the best option to minimize the BER.

The performance obtained with the probabilistic algorithm confirms as well that considering the retransmission age of the subframes in the allocation of the computation resources may improve significatively the performance of the system, especially in terms of accuracy.

A. Parameter optimization

To allow the comparison between the ILP-based and the probabilistic algorithms we have considered, so far, only binary values for the parameters ( , α, β). In this subsection we relax this requirement and we allow ( , α, β) to take real values in the interval [0, 1] 3 , to investigate whether better performance trade-offs are possible with the probabilistic algorithm. Because of the normalizing factor in [START_REF] Qian | Baseband processing units virtualization for cloud radio access networks[END_REF] the different strategy operated by the probabilistic algorithm depends on the relative magnitudes of the elements in ( , α, β) and not on their absolute values, so that restricting the dynamics to [0, 1] is done without loss of optimality.

We focus on the case of K = 1 and |N | = 30, and we simulate the behavior of the probabilistic algorithm for various configurations of the triple ( , α, β). Figure 3 represents the achievable BER at MAC layer, as a function of the corresponding BRR at the PHY layer. Each dot in the scatter plot corresponds to a configuration of ( , α, β). The plot shows that the previously considered cases roughly describe the boundaries of the regions of the achievable trade-offs. The dynamic of the BER axis in Figure 3 spans about 10 dB, which indicates that the choice of the parameters may greatly affect the accuracy of the algorithm. As already suggested by Figure 1, the strategy ( , α, β) = (0, 1, 1) minimizes the BER. From Figure 3 is evident that optimizing the accuracy at the PHY layer (red dot) leaves some potential untapped, and choosing a cross-layer strategy where also the HARQ retransmission age is considered allows to gain up to 5 dB.

By looking at Figure 3 the strategies ( , α, β) = (0, 1, 0) (blue dot) and ( , α, β) = (0, 1, 1) (purple dot) appear equivalent. Figure 4 shows the trade-off achievable between BER and Goodput, and shows that the cross-layer strategy ( , α, β) = (0, 1, 1) is able to minimize the BER while very nearly achieving the maximum Goodput. It is however worth noticing that the maximum improvement in Goodput achievable by varying the parameters is of about 2%. This confirms that the choice of the strategy is most critical with respect to accuracy. Finally, the position of the yellow dot in Figure 4 shows that the policy of limiting the subframes losses at the PHY layer, however a natural choice, achieves one of the least satisfying performance trade-off.

VI. CONCLUSION

We have considered computing resources allocation for the uplink in a C-RAN architecture. When the system is in overload, it is necessary to draw a policy to decide which subframes will not be processed. We have considered a system where the computation resources are allocated separately from the radio resources. Minimizing the data losses at PHY layer, although a very natural strategy, has been proven suboptimal when the performance of the system is gauged at the upper layer. A cross-layer strategy accounting also for the HARQ retransmission process at the upper layer has allowed to sensibly improve the performance, especially with respect to accuracy.

We have considered here a simplified setting where each subframe hosts data of one user. In real systems the same subframe may simultaneously host data of multiple users. The probabilistic algorithm can be adapted to this case, by extending the values that the tag r i may take to account for the "efficient normalized age" of the subframe.

This study showed that the cross-layer strategy may improve the overall spectral efficiency. This suggest that tackling the scheduling of the radio and the computing resources jointly is a good direction for future work.

Fig. 1 .

 1 Fig. 1. PHY-layer performance of the scheduling algorithm via ILP.

Fig. 2 .

 2 Fig. 2. MAC-layer performance of the scheduling algorithm via ILP.

Fig. 3 .

 3 Fig. 3. Achievable BER at MAC layer as a function of the BRR at the PHY layer (bottom), varying the parameters of the probabilistic algorithm.


Damien Besancenot
email: damien.besancenot@parisdescartes.fr.z

Radu Vranceanu
email: vranceanu@essec.edu.

PROFESSION AND DECEPTION: EXPERIMENTAL EVIDENCE ON LYING BEHAVIOR AMONG BUSINESS AND MEDICAL STUDENTS

Keywords: JEL Classi…cation: C91, D83, I19 Lies, deception, communication, medicine, business administration, survey data

This paper reports data from a sender-receiver experiment that compares lying behavior between two groups of students, one in business administration and the other in medicine. We use a modi…ed version of the sender-receiver deception game introduced by Erat and Gneezy (2012) to collect data on 393 subjects. The results show that both groups of students respond to incentives as expected: the frequency of lying is higher, the higher the bene…t for the sender, and the lower the loss for the receiver is. For given payo¤s, there is little di¤erence between the two groups in the domain of white lies; however, business students resort to sel…sh lies more frequently than do medical students. Furthermore, the analysis does not con…rm di¤erences in altruism between the two groups.

Introduction

Research on lying and deception has surged in the last …fteen years, driven by a rising awareness of how important dishonest communication can be in shaping economic and political outcomes, particularly in the era of unveri…able Internet news. In contrast to previous studies developed by psychologists on the motives and emotional consequences of false messages,1 experimental economists have developed a set of studies emphasizing the material consequences of such ethically challenging behavior.

A fundamental typology of lies with respect to the material consequences of a lie in a sender-receiver game has been introduced by [START_REF] Erat | White lies[END_REF], following a pathbreaking paper in the research on lies by [START_REF] Gneezy | Deception: The role of consequences[END_REF]. 2 In this setting, lies have a strategic purpose: the sender issues a false message with the aim of in ‡uencing beliefs and the actual response of the receiver. 3 In general, the literature refers to a sel…sh black lie as a situation in which a false statement issued by the sender prompts the receiver to take an action that improves the well-being of the sender and deteriorates the well-being of the receiver.

These sel…sh lies are ubiquitous in the world of business and are part of many commercial negotiations, with sellers overestimating costs, and buyers understating their true willingness to pay [START_REF] Schweitzer | Curtailing deception: The impact of direct questions on lies and omissions[END_REF][START_REF] Aquino | Lying in negotiations: How individual and situational factors in ‡uence the use of neutralization strategies[END_REF][START_REF] Gneezy | Deception: The role of consequences[END_REF][START_REF] Chelliah | Deception and lies in business strategy[END_REF]. [START_REF] Erat | White lies[END_REF] focus on the more ethically ambiguous white lies, where the false message is bene…cial to the receiver, and further distinguish between Pareto white lies from which both the sender and the receiver bene…t, and altruistic white lies, whereby the sender sacri…ces some of his/her bene…t for the bene…t of the receiver.

In this paper we compare the strategic lying behavior of two groups of people exposed to di¤erent professional norms and social expectations: students of business administration and students of medicine. While lying behavior of business students has already been analyzed by a number of studies, the lying behavior of medical students is unknown. The paper thus aims to contribute to both the literature on lying and deception and to a growing literature on behavioral health economics [START_REF] Cox | Experimental and behavioral economics of healthcare[END_REF][START_REF] Galizzi | Behavioral experiments in health economics[END_REF].

People who select into di¤erent professions have di¤erent motives and behave di¤erently.

Taking a simpli…ed view, in the world of business, people are expected to pursue their own objectives with no restrictions other than the law, while the competitive market mechanism coordinates their self-interested choices towards the common interest. Individuals are expected to exploit any trading opportunity, and this is morally justi…ed by the contribution to higher national wealth. Furthermore, rents of any sort can only be ephemeral, as competition should spread the bene…t among the many (inter alia, [START_REF] Hayek | The use of knowledge in society[END_REF]Von Misses, 1949). 4In this context, business people and students in business administration are supposed to embrace a materialistic mindset, endorsing a preference for competition, performance seeking and limited pro-sociality [START_REF] Holland | Making Vocational Choices: A Theory of Careers[END_REF][START_REF] Vansteenkiste | Materialistic values and well-being among business students: Further evidence of their detrimental e¤ect[END_REF]. 5 Lies among traders who negotiate can be tolerated since, ultimately, competition guarantees the emergence of the market price at which social welfare is highest. Empirical research tends to corroborate these predictions about dishonest communication. [START_REF] Mccabe | Cheating among business students: A challenge for business leaders and educators[END_REF] report higher self-reported frequencies of cheating on exams among undergraduate business than among students in other …elds (including medical studies). 6 Other studies suggest that students in business and economics engage more easily in sel…sh lying than subjects in other …elds, such as humanities or engineering [START_REF] Lundquist | The aversion to lying[END_REF][START_REF] Lewis | Drawing the line somewhere: An experimental study of moral compromise[END_REF][START_REF] Raul | Do economists lie more?[END_REF].

The medical profession is supposed to build on a fundamental moral principle -primum non nocere (…rst, do no harm) -a moral imperative that can be traced back at least to Epidemics (2, 4-7), the well-known book written by Hippocrates in 410 B.C. [START_REF] Beauchamp | Principles of Biomedical Ethics[END_REF][START_REF] Hoerni | L'éthique médicale. Principales évolutions au …l des siècles[END_REF]. In line with this norm, it is widely believed that the medical profession attracts intrinsically motivated people with strong pro-social values [START_REF] Brock | Generosity and prosocial behavior in healthcare provision evidence from the laboratory and …eld[END_REF], including a high degree of altruism or concern for patients'health [START_REF] Arrow | Uncertainty and the welfare economics of medical care[END_REF][START_REF] Ellis | Provider behavior under prospective reimbursement: Cost sharing and supply[END_REF][START_REF] Balsa | Prejudice, clinical uncertainty and stereotyping as sources of health disparities[END_REF]. However, the medical profession has its own ‡aws: a vast body of literature reveals that physicians respond to incentives like any other human being; furthermore, medical advice can be subject to con ‡icts of interest building on physicians' sel…shness, a weakness that some large pharma can exploit to the expense of the patients or health insurance [START_REF] Sah | Physicians under the in ‡uence: social psychology and industry marketing strategies[END_REF][START_REF] King | Gifts and in ‡uence: Con ‡ict of interest policies and prescribing of psychotropic medications in the United States[END_REF].

We consider two main hypotheses to be tested: (1) Because of their strong orientation towards competition and the winner-take-all norm of the profession, business students might be more tempted to tell sel…sh lies, in line with the results of previously cited studies comparing economics students with humanities and engineering students. On the other hand, medical students, following the do-no-harm principle and the higher ethical norms speci…c to their profession, might be less prone to telling sel…sh lies. (2) The degree of altruism is expected to be higher in the population of medical students. This could, in turn, explain a higher propensity to tell white lies among medical students.

The core task of our experiment is similar to that of [START_REF] Erat | White lies[END_REF] (or hereby MBA students than law students. inafter EG2012). There are a sender and a receiver, and two payment options, Option A and Option B, each providing speci…c payo¤s to the two players. Only the sender knows the payo¤s associated with each option. The receiver knows that there are payo¤s associated with an Option A or B, but does not know what these payo¤s are. At the onset of the game, the sender learns that the roll of a die issued a number, let us say 2. He/she can honestly convey the information to the receiver, or give him/her false information, i.e., disclose any other number between 1 and 6. With this information, the receiver can select any number between 1 and 6. If the selected number is the true number (i.e., 2), they both win the payo¤s from Option A; otherwise, they both win the payo¤s from Option B. As we explain later in more formal terms, in this game with a complex message space, a sender who assigns a probability of at least 1/6 to the event that the receiver will follow his/her recommendation should tell the truth if he/she prefers Option A over Option B, and should lie in the opposite case. It is likely that the large majority of senders fall in this category.

We test for …ve conditions, each with its own set of payo¤s, corresponding to an altruistic white lie, two Pareto white lies, and two sel…sh lies. Three of these conditions are exact replicas of [START_REF] Erat | White lies[END_REF], and two of them are di¤erent. These within-subject choices are made by one group of business students and one group of medical students. We also elicit (self-reported) risk tolerance and the degree of altruism by means of a charity giving task.

In brief, our results do not con…rm the higher-altruism assumption for medical students compared to business students. With respect to lying behavior, medical students are not more prone to telling a white lie than business students. However, there is a substantial di¤erence between the two populations in the domain of sel…sh lies; the frequency of sel…sh lies is 20% higher in the population of business students than in the population of medical students. This lie-speci…c di¤erence in lying behavior might be explained by business and medical students di¤ering not in their own perceptions of right and wrong, but in their beliefs about what the other members of their group believe to be right or wrong [START_REF] Spiegelman | What are we really teaching them? Testing the socialization of a maximizing mindset[END_REF].

In this context, business and medical students can have the same aversion to white lies, yet business students, unlike medical students, could consider sel…sh lies to be normal practice within their profession.

The participants in our experiment are …rst-year students in French business and medicine schools. Thus, the experiment tests the preferences of the students who self-select into two di¤erent professions. It goes beyond the purpose of this paper to reveal all the motives that drive their decision. In a complementary analysis, we carry out a survey on a representative sample of the French population to capture the beliefs of the general public about the lying behavior of the two pro…les of students. The results of the survey reveal signi…cant coherence between the lying behavior observed in the lab and general opinion. A form of dynamic equilibrium, where beliefs drive students' of a given type towards a profession, and these career choices are validated by their behavior, could be one candidate mechanism for the observed behavior in the lab. A similar argument was submitted by [START_REF] Schneider | Sorting and wage premiums in immoral work University of Zurich[END_REF] who reveal from lab data and national surveys in Switzerland that individuals who are least concerned with acting morally self-select into jobs generally perceived as immoral.

While students might identify with their future on-the-job decisions [START_REF] Hennig-Schmidt | How payment systems a¤ect physicians'provision behaviour-an experimental investigation[END_REF], socialization through education (Rako et al., 2017;[START_REF] Spiegelman | What are we really teaching them? Testing the socialization of a maximizing mindset[END_REF] and internalization of professional norms [START_REF] Ahlert | Which patients do I treat? An experimental study with economists and physicians[END_REF]Kestenrich et al., 2015) can alter preferences and thus shape the behavior of future professionals in the two …elds. As a path for future research, it would be interesting to study whether our results hold in an experiment involving last-year students or professionals instead of …rst-year students.

A known limitation of the within-subject design is that subjects might use information from early tasks in the experiment to second-guess and update their answers in later tasks. However, while this criticism may apply within one group of students, the analysis focuses essentially on the comparison between medicine and business students who were exposed to identical choices (in a between-subject setting). As a bene…t of the within-subject design, we were able to elicit important subject characteristics such as altruism and risk tolerance and use them as controls in our analysis. We also ensured that we collected a relatively large number of observations to limit the measurement error problem.

Review of literature

A substantial body of evidence with elementary deception games has established that some persons resist the temptation to lie regardless of the potential bene…ts and that those who do lie do not push the lies to extreme limits, even if the subjects forgo positive gains by doing so.7 Furthermore, it has been shown that many people refrain from lying even if this action is bene…cial to the receiver of the information [START_REF] Erat | White lies[END_REF][START_REF] Cappelen | When do we lie?[END_REF][START_REF] Biziou-Van-Pol | Does telling white lies signal pro-social preferences?[END_REF]. These results suggest that humans have some form psychological cost of lying, which could be grounded in the self-image of the person (Ellingsen and Johannesson, 2004;[START_REF] Gneezy | Deception: The role of consequences[END_REF][START_REF] Vanberg | Why do people keep their promises? An experimental test of two explanations[END_REF][START_REF] Gneezy | Bribing the self[END_REF] or in how others see him/her, whether directly in terms of reputation [START_REF] Mazar | The dishonesty of honest people: A theory of self-concept maintenance[END_REF][START_REF] Tergiman | The way people lie in markets[END_REF] or unful…lled expectations (Charness and Dufwemberg, 2006;[START_REF] Dufwenberg | Lies in disguise -A theoretical analysis of cheating[END_REF][START_REF] Gneezy | Lying aversion and the size of the lie[END_REF][START_REF] Khalmetski | Disguising lies-Image concerns and partial lying in cheating games[END_REF], or multiple combinations of these motives as analyzed in [START_REF] Abeler | Preferences for truthtelling[END_REF].

In the last few years, a substantial body of experimental research has emerged to test the extent of altruism among medical students. [START_REF] Hennig-Schmidt | How payment systems a¤ect physicians'provision behaviour-an experimental investigation[END_REF] use a lab experi-ment to compare medical students'behavior under the fee-for-service (FFS) and capitation (CAP, which is a …xed payment per patient) models and …nd results that can be explained only if subjects present a substantial degree of concern about the patients' well-being. 8Godager and Wiesen (2013) use the data set from [START_REF] Hennig-Schmidt | How payment systems a¤ect physicians'provision behaviour-an experimental investigation[END_REF] to estimate the (positive) weight of patients'utility in the physician's own utility function. [START_REF] Martinsson | Physician behavior and conditional altruism: the e¤ects of payment system and uncertain health bene…t[END_REF] show that the weight of patients'utility varies with the severity of the disease, itself related to the physician's system of priorities. While the assumption of physicians'altruism seems to be corroborated by this evidence, the question of whether physicians (or medical students) are more or less altruistic than individuals in other categories is still unsettled. Brosig-Koch et al. ( 2017) compare the decisions of medical students with those of business students in a similar experiment and …nd evidence that non-medical students are less altruistic albeit with signi…cant heterogeneity. [START_REF] Ahlert | Which patients do I treat? An experimental study with economists and physicians[END_REF] compares the distributive preferences of medical and economics students and …nds evidence that, in an unframed setting, economists choose more often the individualistic pro…t-maximizing allocation. In contrast with these results, [START_REF] Li | Social preferences of future physicians[END_REF] study choices in a standard dictator game and …nd no di¤erence in altruism between medical students and the general population or similar law students.

There is substantial literature, surveyed in [START_REF] Searight | Physician deception and telling the truth about medical "bad news": History, ethical perspectives, and cultural issues[END_REF] on the scale and scope of deceptive communication in physician-patient communication. These authors explain that traditionally, physicians tend to avoid blunt communication of bad news and often hide or attenuate it, even in cases in which truth-telling can actually improve the condition of the patient. 9 Such behavior can be rationalized if prosocial lies are perceived as "more moral" than telling the truth [START_REF] Levine | Are liars ethical? On the tension between benevolence and honesty[END_REF][START_REF] Levine | The surprising costs of silence: Asymmetric preferences for prosocial lies of commission and omission[END_REF], or if physicians develop compassion with respect to the di¢ cult situation of the patient [START_REF] Lupoli | Lying because we care: Compassion increases prosocial lying[END_REF].

Despite the obvious importance of these issues, experimental studies on lying behavior among physicians and medical students are rather scarce. As a notable exception, Hennig-Schmidt et al. ( 2018) built a framed experiment to analyze diagnosis-related group upcoding in neonatology, comparing the reporting by business and medical students. In the absence of audits and sanctions, overreporting (which leads to higher payo¤s) is the dominant strategy (with 70% of participants engaging in overt dishonesty); furthermore, medical students appear to be more prone to overreporting than economics students (the trend, however, reverses when controls are introduced).

Prosocial preferences should be an important determinant of lying behavior. For instance, altruism could restrain the desire to state a sel…sh black lie that would deteriorate the wellbeing of the receiver of the information. [START_REF] Cappelen | When do we lie?[END_REF] and [START_REF] Biziou-Van-Pol | Does telling white lies signal pro-social preferences?[END_REF], using experimental data, show that the aversion to telling a Pareto white lie is stronger among altruistic individuals. 10 The latter study also shows that altruistic people are more prone to telling an altruistic white lie. 11 The paper is organized as follows. The next section introduces the experimental design.

The results of the experiment are presented in Section 3. Section 4 summarizes the results of the survey on the representative sample of the French population. The last section o¤ers our conclusion.

Experimental design

The paper and pen experiment was administered in a classroom setting. The sample comprised 178 subjects in their …rst-year of medical studies in a high-pro…le medical school in Paris, France, and 163 …rst-year students in business administration in an equivalently ranked business school in the same geographic area. Students attending regular classes at one of the two institutions were asked twenty minutes before the class break whether they wished to participate in the experiment and had the option to leave the classroom. The sessions took place between October and December 2019. The instructions were very close to those in the EG2012 within-subject design. 12 The core task is the deception game used in that paper enriched by two additional conditions, to which we add complementary tasks to measure risk tolerance and altruism (see the Appendix for the instructions).

Speci…cally, this lying game involved a sender and a receiver. The experiment featured two main stages. First, a paper questionnaire was distributed to a group of students in the sender role. The participants were informed that they would be paired within one week with a receiver: "he/she is a student like you, from another higher education institution". We used this general statement to rule out professional socialization or homophyly. The receivers were students in the other school. Similar to EG2012, one in twenty pairs were selected at random to be paid in cash within the three weeks after the senders'decision took place. On average, senders earned 23.8 euros, and receivers obtained 25.7 euros.

The paper questionnaire for the senders contained the main task. The senders were told that at the onset of the experiment, a six-sided die was rolled, and we communicated the outcome to the sender. The sender was presented with …ve payment possibilities or conditions, each including payment Option A (s A ; r A ) and payment Option B (s B ; r B ) in which s A , s B were the sender's payo¤s, and r A , r B were the receiver's payo¤s. The sender was informed that the payment in each condition depended on the choice made by the receiver. If the receiver chose the true outcome of the die roll (unknown to him/her), Option A would be implemented; otherwise, option B would be implemented. For each condition, the sender sent a message that "The outcome of the roll of the die was i ". The receiver had no other information than this statement. From the instructions, he/she knew that there were payo¤s associated with each option but had no idea what these payo¤s were.

At the end of the experiment, one of the …ve conditions was selected at random for payment in cash.

Table 1 summarizes the payo¤s by condition. 13 Each subject had to make a choice for each scenario. [START_REF] Sutter | Deception through telling the truth?! Experimental evidence from individuals and teams[END_REF] brings into the picture the interesting concept of "sophisticated deception".

Condition

He studies the sender-receiver game by [START_REF] Gneezy | Deception: The role of consequences[END_REF] in which the message space includes only one true message and only one false message. In this context, a dishonest individual who assigns a subjective probability > 0:5 that the receiver will follow an opposite recommendation to the one given, would tell the truth when he/she actually seeks deception.

Erat and Gneezy (2012) explain that in the more complex message space with six possible statements only one being true, such a sophisticated deception is improbable. Their argument is quite compelling. Let U A be the utility of the sender from Option A, and U B his/her utility from Option B. Option A is implemented if the receiver chooses the true number, and Option B is implemented if he/she chooses a di¤erent number. Denote now by p the probability assigned by the sender to the event that the receiver does not follow his/her recommendation.

If the sender tells the truth (dice_nb = 2), the expected utility is:

E[truth] = (1 p)U A +pU B :
If the sender sends a false message (dice_nb 6 = 2), the expected utility is

E[lie] = (1 p)U B + p(4=5U B + 1=5U A ).
Let us assume that the sender prefers Option B to Option A, i.e.,

U B > U A : It is easy to check that for U B > U A ; E[lie] > E[truth] if (1 p) > 1=6 or p < 5=6:
This person would lie if the probability that the other follows his/her recommendation is

(1 p) > 1=6, which, as argued by [START_REF] Erat | White lies[END_REF], is a plausible assumption for a majority of senders.

In our experiment, 40% of the receivers followed the sender's recommendation, which is more than 16.7% (p-val<0.01). If the actual frequency is a good proxy for the expected probability of implemented recommendations, senders should lie about the number on the die if they prefer Option B to Option A, and vice versa.

Stating that the roll of the die was di¤erent than the actual number is a lie that the sender delivers with the purpose of making the receiver choose Option B. Given the change in payo¤s, T [ 1; 10] corresponds to an altruistic white lie (the sender sacri…ces 1 euro for the bene…t of the receiver), T [1; 10] and T [10; 10] correspond to Pareto white lies, and T [1; 5] and T [10; 5] correspond to sel…sh black lies, i.e., the sender is aware that his/her gain also involves a loss for the receiver.

After making the choice of the number to communicate (sender) or the number to select (receiver), each participant was instructed to move to the second part of the experiment, which was independent of the …rst part. The instructions for the second part were delivered in a sealed envelope, to avoid any in ‡uence of the second part task on the …rst.

After indicating their age and gender, participants were asked to report their risk tolerance on the scale introduced by [START_REF] Dohmen | Individual risk attitudes: Measurement, determinants, and behavioral consequences[END_REF]. The question used is as follows:

Thinking of yourself, do you think you are fully prepared to take risks? Subjects could answer from 1, for "not at all", ..., to 5, for "very much". Answers were converted into a (0;1) risk tolerance index. 14 The last task aimed to determine subjects' degree of altruism. They had learned that they received an additional 10 euros, that they could share with a philanthropic organization from a list of 10 charities, all of them well known in France (we exclude organizations from the health sector; see the list in the Instructions). If the pair of subjects of which they were a part was selected for payment, the amount that they indicated would be transferred to one of the associations from the list, selected at random. This 0 to 10 (euro) donation was also converted into a (0;1) altruism index. The total amount transferred to charities was 160 euros. 15

3 Results [START_REF] Erat | White lies[END_REF].

General results

Even if the lie bene…ts both subjects, approximately 1/4 of the senders never lie, as if they follow some categorical imperative, tantamount to experiencing a very large cost from lying.

The within subject design allows for an additional check that incentives have an impact on the decision to lie. We present contingency tables separately for Pareto white lies (Table 3) and sel…sh lies (4).

In We can now turn our attention to the key research question of the di¤erences between the two professional pro…les. We …rst analyze the di¤erences in personal characteristics and then study the di¤erences in lying behavior. In general, in France medical studies attract a larger proportion of women than do business studies; in the two higher education institutions, women represent 68% and 51% of the total population, respectively, which is re ‡ected in the di¤erent proportions of female subjects across the two groups (p < 0:01). Additionally, the medical students in our sample are one year older than the business students, on average. While the mean measure of altruism is slightly larger in the sample of medical students than in the sample of business students (0.84 vs. 0.79), this di¤erence is not statistically signi…cant (p = 0:13). 16 On average, business students present a higher risk tolerance (p < 0:01). This result might be quali…ed because the sample of business students includes a smaller percentage of women (who, on average, have a lower risk tolerance; see Table 11 in Appendix I). A regression model (unreported) con…rms that this di¤erence in self-reported risk tolerance between the two professions persists after controlling for the gender of the respondent. Comparing the two pro…les, we observe substantial similarities in the domain of white lies and substantial di¤erences in the domain of sel…sh lies, with business students more willing to tell a sel…sh lie. We can con…rm that only the frequencies reported for business students are now very close to those in the data reported by [START_REF] Erat | White lies[END_REF].

Business vs. medical students

A substantial proportion, 21% of the medical students and 26% of the business students, refuse to state a Pareto white lie that increases the payo¤s of both participants by as much as 10 euros.

Students of both pro…les respond to incentives as documented by [START_REF] Gneezy | Deception: The role of consequences[END_REF] and Erat and Gneezy (2012):

At a constant gain for the receiver, the sender lies more often if his/her bene…t is large (in Figure 2, the frequency of lying increases from left to right on a given horizontal line).

At a constant gain for the sender, the sender lies less often when the receiver is losing something compared to when the receiver is gaining something (in Figure 2, the frequency decreases from top to bottom on a given vertical line). However, for business students, no change is observed for the large payo¤.

We can use a regression model to verify whether this pattern holds when controlling for personal characteristics.

Table 7 displays the output of OLS regressions where the dependent variable is a dummy "Lie", which takes the value of 1 if the subject has told a lie in a given condition (i.e., in our case, reported a number di¤erent from 2). Individual data are stacked by condition. There is a dummy variable "Med", taking the value of 1 (0) for medical (business) students, and there is a dummy for each of the …ve conditions, D_T [; ]; taking the value of 1 for that condition, and zero otherwise. The altruistic lie condition (T [ 1; 10]) serves as the benchmark. Other covariates are: gender (female=1), age, self-reported risk tolerance, and the elicited altruism measure. Observations are not independent since each subject provides …ve distinct answers.

To correct for this bias, errors are clustered by subject. 17

Result 1. The results of the regressions corroborate the existence of the incentive e¤ect: Table 7: The "general" lying equation, pooled data as shown by the coe¢ cients of the condition dummies, individuals of both pro…les lie more if their bene…t is increasing at a constant payo¤ for the receiver and lie less if the bene…t to the receiver deteriorates at a small constant gain for themselves (but not for the large gain).

Note that Model 1 is a plain replica of the probabilities displayed in the descriptive statistics in Table 6 (the constant term is the frequency of business students telling altruistic lies).

Including personal characteristics does not greatly alter the elementary proportions.

Result 2. The interaction terms for the Pareto white lies are not statistically signi…cant, revealing no di¤erence between the two types of students with respect to these prosocial lies.

Result 3. There is a signi…cant medicine study e¤ect in the domain of sel…sh lies. Even when controlling for the degree of altruism and risk tolerance, depending on the condition, medical students have an 18% to 20% lower probability of telling a sel…sh lie than business students. This result is consistent with …ndings by [START_REF] Lundquist | The aversion to lying[END_REF], [START_REF] Lewis | Drawing the line somewhere: An experimental study of moral compromise[END_REF] and López-Pérez and [START_REF] Raul | Do economists lie more?[END_REF], who show that students in business and economics tend to engage more easily in sel…sh lying than subjects in other …elds.

We can also perform the same analysis separately for medicine and business students;

the interaction terms are no longer needed. The results con…rm the presence of the incentive e¤ect. Furthermore, medical students appear to react much more strongly to the deterioration of the well-being of the other by reducing their lying: at a bene…t of 1 euros for themselves, with payo¤ change going from 10 euros to 5 euros for the receiver, the average sender who is a medicine student reduces his/her frequency of lying by 31:2% ( 9:8%) = 41%. Moreover, at a payo¤ of 10 euros for themselves, going from 10 euros to 5 euros for the receiver, their frequency of lying falls by 43:4% 15:6% = 27:8%. On the other hand, for the business students, the frequency of lying in the same situations falls by only 27:3% 10% = 17:3% and only 35% 33% = 2%.

Table 9 provides estimates of "condition-speci…c" lying equations, one for each of the …ve scenarios (the subject provides only one answer, for that speci…c condition). For each condition, the dependent variable is a dummy variable taking the value of 1 if the subject has told a lie. The other covariates are similar to those used in the previous regressions. We also include a gender profession interaction term. Table 9: "Condition-speci…c" lying equations These regression models corroborate the previous results and provide new information.

Result 4. The behavior of the students regarding the altruistic white lies (which was the benchmark in the former regressions) follows the same pattern as the behavior regarding the Pareto white lies. More precisely, there is no pro…le e¤ect in the domains of altruistic white lies or Pareto white lies (there is a weak positive e¤ect a¤ecting medical students when their bene…t is large).

Result 5. As expected, altruism has a (weak) limiting e¤ect on sel…sh lies (which deteriorate the income of the receiver). In our data, altruism is not related to the decision to tell a Pareto white lie or an altruistic lie; this result contrasts with the …ndings of [START_REF] Cappelen | When do we lie?[END_REF] and Capraro et al. (2015) who …nd that the aversion to telling a Pareto white lie is stronger among altruistic individuals.

Result 6. These results point out gender e¤ects. [START_REF] Capraro | Gender di¤erences in lying in sender-receiver games: A metaanalysis[END_REF] performed a metaanalysis on 65 sender-receiver deception games and found that men are signi…cantly more likely than women to tell both black and altruistic white lies; the results were inconclusive in the case of Pareto white lies. 19 In our data, the frequencies of men and women telling sel…sh 1 8 Probit estimates reveal similar results.

1 9 As examples of sender-receiver lab experiments showing that men tend to resort to sel…sh lies more often lies are quite similar (see Appendix table 12). However, in the T [1; 5] sel…sh lie model, the coe¢ cient of the interaction term between gender (female) and …eld of study (medicine) is negative, showing that women studying medicine have a higher reluctance to tell sel…sh lies.

This result is in line with López-Pérez and Spiegelman (2019), who …nd that women studying business and economics engage more often in sel…sh lies than do women in other …elds.

Beliefs and actual behavior: survey data

These lab experiments allowed us to directly observe students'lying behavior and revealed signi…cant di¤erences. The sample included only …rst-year students who had not been exposed to intensive speci…c training. Thus, the observed lying behavior can be related to the motives that prompted them to choose their future profession in the …rst place. Unfortunately, our experiment does not allow us to say much about what these motives may be.

To complement the analysis, we asked the survey institute OpinionWay to provide a report on how the general public of France perceives the lying behavior of the two groups of students. To keep the complexity and number of questions relatively low, in the survey, we focused on the polar cases of sel…sh black lies and altruistic white lies (Pareto white lies were omitted). Four speci…c questions were included in the omnibus weekly survey. Data collection was carried out on July 2nd, 2020. The sample of 1056 respondents is representative of the French population of 18 years or more. 20 In total, 2% of polled persons did not answer our questions, which yields 1035 valid answers. Respondents received a …xed reward or could opt for a gift to the charity of their choice.

The questions are as follows:

than women do, see: [START_REF] Gill | Cheating in the workplace: An experimental study of the impact of bonuses and productivity[END_REF][START_REF] Conrads | Lying and team incentives[END_REF][START_REF] Dreber | Gender di¤erences in deception[END_REF][START_REF] Erat | White lies[END_REF][START_REF] Kleinknecht | A man of his word? An experiment on gender di¤erences in promise keeping[END_REF] Table 10 presents the synthesis of the results that consolidates all a¢ rmative (5 to 7), and all negative (1 to 3) answers (the seven-category distribution is presented in Appendix Table 13). The last column presents the output of a z-test for one proportion of the nonneutral observations.

At In the experiment, there was no di¤erence between the two groups of students with respect to prosocial lies. In the survey, a majority of the respondents (53.9%) chose the neutral answer, and equal proportions of respondents agree and disagree with the statement that students in medicine are more prone than students in business to tell white lies.

However, only a small number of respondents (9.8%) agreed that medical students are more tempted to tell sel…sh lies, compared to 36.3% who disagreed. This skewed distribution of the opinions is in line with the results of the experiment showing that, on average, business students tell sel…sh lies more often than medical students.

With respect to their opinion on the use of the two types of lies in the two professions, the respondents consider that sel…sh lies are more frequent in the business world than in the medical sector (43.8% agree while only 15.2% disagree); the opinions reverse for the case of white lies (36.4% disagree while 19.4% agree). According to these "folk beliefs", the business profession in general provides a more fertile ground for sel…sh lies; on the other hand, the medical profession provides a more supportive environment for white lies. [START_REF] Schneider | Sorting and wage premiums in immoral work University of Zurich[END_REF] have shown that immoral work attracts those workers least concerned with acting morally, which in turn can deteriorate the moral standards of some professions. This could be a possible explanation for why students of a given lying pattern self-select into one of the two professions: if people in general believe that, for example, in the business world sel…sh lies are the norm, those with a taste for sel…sh lies may be likely to choose that profession. Furthermore, if people with a taste for sel…sh lies self-select into the business profession, over time, this profession will comprise more people of this type than the medical profession, which validates the beliefs of the general public. This set of beliefs and actual profession choices can be de…ned as self-ful…lling prophecies (Nash Bayesian equilibrium).

Conclusion

In the last …fteen years, the literature in experimental economics on lies and deception has expanded at a steady pace. This paper analyzes the di¤erences in lying behavior between two groups of subjects exposed to di¤erent professional norms, expectations and stereotypes, namely, business and medical students.

In the world of business, many professionals …nd it legitimate to exploit any trading opportunity, including a would-be informational advantage. Economists like to believe that strong competition among …rms rules out systematic rent extraction but are relatively silent about the ethical consequences of trading with a player who has market power. However, lying in negotiations, with sellers exaggerating costs and buyers understating their willingness to pay, is a common practice. For many trading people, a "good" deal is one in which one party obtains most of the surplus from trade at the expense of the other and sometimes in sheer disregard of the interest of the other. In contrast, centuries of medical practice throughout history reveal that physicians seldom exploit their informational advantage and act in the interest of the patients even at personal cost. Such behavior is grounded in the professional norms inspired by the Hippocratic oath, according to which the interest of the patient should always prevail. In turn, these professional norms should attract the most pro-social persons to this …eld. Sel…sh lies are not tolerated, while some white lies, such as prescribing a placebo or hiding very bad news, could be common. Of course, these stereotypes have their own exceptions in both worlds. In the health sector in particular, con ‡icts of interest and the hiding of medical errors have sometimes been revealed.

The experiment presented in this paper allowed us to directly observe the lying behavior of the respective groups. We used the classic sender-receiver deception game by [START_REF] Erat | White lies[END_REF] to determine and assess the importance of those behavioral di¤erences. The complementary giving-to-charity task did not reveal any substantial di¤erence in altruism between the two groups; however, business students present a higher risk tolerance.

Turning to the strategic communication issue, it turns out that students of both pro…les respond to incentives, as documented in [START_REF] Gneezy | Deception: The role of consequences[END_REF] and [START_REF] Erat | White lies[END_REF]. However, while many students lie, a nonnegligible share of both medicine and business students refuse to tell even a Pareto white lie, which would deliver signi…cant gains to both parties.

The propensity to tell white lies was similar between the two groups. On the other hand, medical students appear to be signi…cantly more reluctant than business students to tell selfish lies, a result that holds when controlling for altruism and risk aversion. Medical students exhibit a higher concern that their partner will be harmed by misleading communication.

The fact that both types of students behave in the same way in terms of telling white lies but di¤er with respect to sel…sh lies is troubling. If moral people just dislike lying, regardless of the consequences for others, then there should be no di¤erences between the two groups for both types of lies. The results point to some di¤erences in student's perceptions of how harmful or legitimate the use of sel…sh lies can be, with business students telling sel…sh lies more easily than medical students.

A representative survey of the French population, conducted in July 2020 by OpinionWay for the purpose of this paper, revealed that the general public of France expects sel…sh lies to be more frequent in the business sector than in the medical sector, the opposite holding for white lies. The general public tends to believe that the frequency of sel…sh liars is higher among business students than among medical students. These results match the behavior observed in the experiment, and might suggest one among many possible explanations of why young people self-select for a given profession. If telling sel…sh lies is the norm in the business world but not in medicine, students with a taste for sel…sh lies would enroll in business studies, and those who are more averse to sel…sh lies would enroll in medicine.

It is very di¢ cult to draw any moral criticism or lesson from the evidence provided in this paper since each profession has its own communication norms. However, from a methodological point of view, it is important to keep in mind that results obtained from samples of students in business and economics, which are the main groups of the public considered in economics lab experiments, might not be representative of the deception behavior of the general population. To strengthen the external validity of these studies, it might be useful to perform replication studies of the main deception experiments on di¤erent types of subjects.

A.2 Instructions for the Sender

Introduction.

Welcome to this short experiment.

Please read these instructions carefully. You may earn a considerable sum of money, depending on the decisions you make in the experiment. The amounts in euro are presented here below. At the end we'll chose one in 20 participants and pay them in cash at the end of the experiment (no later than 2 weeks from now on).

You will be matched at random with another participant that will take his/her decision in a second stage. The other subject is a student in a di¤erent higher education institution.

His/her identity will not be revealed to you, and he/she will not know who you are. All answers will be traded with the highest degree of privacy.

At the end of the form there is a 4 digit ticket. The number was generated at random.

Please keep it, the ticket will help us call the subjects for the payment in this same room, after two weeks. The payment is executed in cash, and privately.

From now on, please stay focus and don't talk to each other.

The main task

Before starting this experiment, we have rolled a 6-sided die, and obtained the outcome 2.

The other participant will not be informed that the outcome of the die roll was 2. However, he or she will be told that you have been informed about the outcome of the die roll. There are …ve di¤erent payment possibilities. Only you will be informed of the particular monetary values in each payment option. The other participant will not be informed of these monetary values. However, he or she will be told that you have been informed of these monetary values.

At the end of the experiment, we will choose one of these payment possibilities at random for actual payment.

For each of the payment possibilities, we now ask you to send a message to the other participant. The message will correspond to a number from 1 to 6. There are six possible messages:

Message 1: "The outcome from the roll of the 6-sided die is 1."

Message 2: "The outcome from the roll of the 6-sided die is 2."

Message 3: "The outcome from the roll of the 6-sided die is 3."

Message 4: "The outcome from the roll of the 6-sided die is 4."

Message 5: "The outcome from the roll of the 6-sided die is 5."

Message 6: "The outcome from the roll of the 6-sided die is 6."

Your message will be shown to the other participant, and then he or she will be asked to choose a number between 1 and 6.

The choice of the number by the other participant will determine the payments in the experiment.

Payment possibility #1

If he or she chooses the actual outcome of the roll of the dice, 2, then you will receive $20 and he or she will receive $20.

If he or she chooses a number di¤erent than the actual outcome, you will receive $19 and he or she will receive $30.

The message I will send in this payment option is "The outcome from the roll of the 6-sided die is ______."

(Please …ll in a number from 1 to 6.)

Payment possibility #2

If he or she chooses the actual outcome of the roll of the dice, 2, then you will receive $20 and he or she will receive $20.

If he or she chooses a number di¤erent than the actual outcome, you will receive $30 and he or she will receive $15

The message I will send in this payment option is "The outcome from the roll of the 6-sided die is ______."

Complementary tasks

The main task is over now, you can move to the complementary tasks. Please open now the envelope.

This last task is completely unrelated to the previous tasks.

If you are one of those chosen for payment, you obtained 10 more euros. You can chose to share it with a charity, to be selected at random from the list of these seven charities. We will transfer the funds at the end of the experiment.

Les

  within-brackets label of the conditions indicates the change in payo¤ s for the two players in Option B relative to their payo¤ in Option A, T [(s B s A ) ; (r B r A )]. For instance, condition T [ 1; 10] means that the implementation of Option B provided the receiver with a bene…t of 10 euros and a 1 euro loss to the sender compared to the payo¤s in Option A.

  the Pareto white lie situation, 62 of the 113 subjects who tell the truth in T [1; 10] switch to lying in T [10; 10] when their bene…t from lying increases. A much smaller number (28 subjects) have the counterintutive reaction of telling the truth in T [10; 10] yet switching to lying in T[1,10]; ( 2 = 45:5; p < 0:01).

  You have received a sealed envelope. You can open it now and read the additional instructions. Please indicate us: your gender M/F Please indicate us: your ageThinking of yourself, do you think you are fully prepared to take risks? Answer on this scale, from 0: "not at all", to 10: "fully prepared".

Table 1 :

 1

		Option A	Option B
		(s A ; r A )	(s B ; r B )
	1. T [ 1; 10] (20,20)	(19,30)
	2. T [1; 10]	(20,20)	(21,30)
	3. T [10; 10] (20,20)	(30,30)
	4. T [1; 5]	(20,20)	(21,15)
	5. T [10; 5] (20,20)	(30,15)

Payo¤s by condition (euros)

If option A was chosen, then both players received 20 euros. If option B was chosen, the payo¤s were unequal, with gains/losses for the two players as displayed in the table. The

Table 2 :

 2 Table2reports the frequencies of liars (senders who communicate a number other than the true one) in the overall sample (mixed population) and compares our results with the results in[START_REF] Erat | White lies[END_REF]. The latter use undergraduate students taking classes in management as subjects. The similarities in our two sets of results are notable in the domain of Pareto white lies (T [1; 10], T [10; 10]). A notable di¤erence is observed in the domain of sel…sh lies (T [1; 5]), with a lower frequency of liars in our sample. Later we show that this outcome is related to the behavior of medical students. A comparison with

		EG2012 (N=58) This study (N=341)
	1. T [ 1; 10] 43%	38%
	2. T [1; 10]	66%	67%
	3. T [10; 10] 76%	77%
	4. T [1; 5]	52%	38%
	5. T [10; 5] n.a.	62%

Table 3 :

 3 Contingency table: Pareto white liesIn the sel…sh lie situation, 99 out of 212 subjects switch from telling the truth to lying for a higher bene…t (at the same cost to the receiver); only 16 subjects lie in T [1; 5] and tell the truth in T [10; 5] when lying brings them a larger bene…t ( 2 = 57:0; p < 0:01).

		T [10; 10]
		Truth Lie Total
	T [1; 10] Truth 51	62	113
	Lie	28	199 227
	Total 79	261 340
		T [10; 5]
		Truth Lie Total
	T [1; 5] Truth 113	99	212
	Lie	16	113 129
	Total 129	212 341

They could belong to a special category of moral subjects who lie if there is a clear bene…t to the other participant, but not when they obtain the same bene…t.

Table 4 :

 4 Contingency table: Sel…sh lies

Table 5 :

 5 Personal characteristics by pro…le (s.e.)

	Table 5 presents the key personal characteristics of the two populations of medicine and
	business students.
		Gender (Fe=1) Age	Altruism (0-1) Risk tol. (0-1)
	Medicine students (N=178) 0.70 (0.04)	19.78 (0.23) 0.84 (0.02)	0.53 (0.02)
	Business students (N=162) 0.41 (0.04)	18.43 (0.11) 0.79 (0.02)	0.64 (0.02)
	Total (N=341)	0.56 (0.03)	19.13 (0.13) 0.81 (0.02)	0.58 (0.02)

Table 6

 6

		Medicine	Business	(p-val)
		(N=178)	(N=163)	di¤. between m/b
	1. T [ 1; 10] 36%	39%	(0.53)
	2. T [1; 10]	67%	66%	(0.79)
	3. T [10; 10] 79%	74%	(0.28)
	4. T [1; 5]	27%	50%	(0.00)
	5. T [10; 5] 53%	72%	(0.00)

presents the proportions of senders who lie, by type of lie (the …ve conditions) and sender pro…le.

Table 6 :

 6 Proportion of senders who lie by type of lie and professional pro…le

  Table 8 presents the results of OLS regressions, with errors clustered by subject.

		Medicine students	Business students
		Model 1	Model 2	Model 1	Model 2
	D_T [1; 10]	0.312*** (0.04) 0.312*** (0.04) 0.273*** (0.05) 0.281*** (0.05)
	D_T [10; 10] 0.434*** (0.05) 0.434*** (0.05) 0.350*** (0.05) 0.358*** (0.05)
	D_T [1; 5]	-0.098* (0.05)	-0.098* (0.05)	0.100* (0.05)	0.101* (0.05)
	D_T [10; 5] 0.156*** (0.05) 0.156*** (0.05) 0.331*** (0.05) 0.333*** (0.05)
	Female (=1) 0.006 (0.05)	0.013 (0.05)	0.048 (0.04)	0.065 (0.05)
	Age	-0.001 (0.01)	-0.002 (0.01)	-0.011 (0.01)	-0.010 (0.02)
	Risk toler.	-	0.146 (0.10)	-	0.161 (0.13)
	Altruism	-	-0.092 (0.07)	-	-0.059 (0.08)
	Constant	0.382**(0.17)	0.390*** (0.17) 0.572** (0.28)	0.491 (0.37)
	N	865	865	799	794
	R2	0.153	0.160	0.082	0.09

Legend: * signi…cant at 10%; ** signi…cant at 5%; *** signi…cant at 1%. Std. err. within parentheses.

Table 8 :

 8 The "general" lying equation

Table 9

 9 reports the output of OLS regressions for each type of lie; 18

		T [ 1; 10]	T [1; 10]	T [10; 10]	T [1; 5]	T [10; 5]
	Age	-0.004 (0.01) 0.010*** (0.00) -0.013** (0.00) -0.006* (0.00)	-0.003 (0.00)
	Altruism	-0.003 (0.09) -0.015 (0.09)	-0.019 (0.04)	-0.141* (0.08)	-0.183* (0.07)
	Risk tol.	0.209 (0.14)	0.232*** (0.04) 0.096 (0.07)	0.131 (0.12)	0.118 (0.16)
	Female (=1)	-0.054 (0.12) -0.068*** (0.01) 0.119 (0.07)	0.107 (0.05)	0.117 (0.10)
	Med. stud. (=1) 0.165* (0.06) 0.063 (0.03)	0.154* (0.07)	-0.217*** (0.03) -0.182** (0.06)
	Female Med	-0.026 (0.04) 0.021 (0.02)	0.126* (0.05)	-0.113** (0.03)	-0.096 (0.05)
	Constant	0.299* (0.11) 0.374** (0.09)	0.877*** (0.05) 0.582 (0.16)	0.797** (0.20)
	N	332	331	332	332	332
	R2	0.03	0.02	0.02	0.07	0.06
	Legend: * signi…cant at 10%; ** signi…cant at 5%; *** signi…cant at 1%. Std. err. within parentheses.

Table 10 :

 10 Opinions on lying di¤erences

	least slight disagreement Neutral At least slight agreement
	S1 36.3%	53.9%	9.8%	p<0.001
	S2 23.0%	54.4%	22.7%	p=0.890
	S3 15.2%	41.0%	43.8%	p<0.001
	S4 36.4%	44.2%	19.4%	p<0.001

Table 13 :

 13 Opinions on lying di¤erences Survey executed by OpinionWay, French representative sample, July 2020.

	1. Fully disagree 2.	3.	4. Neutral 5.	6.	7. Fully agree
	S1 9,1%	16,0% 11,2% 53,9%	5,0%	2,8%	2,0%
	S2 6,2%	8,5%	8,2%	54,4%	12,2% 7,3%	3,3%
	S3 4,2%	5,4%	5,6%	41,0%	12,2% 18,7% 12,9%
	S4 11,9%	15,6% 8,9%	44,2%	8,5%	6,9%	4.0%

See Docan-Morgan (2019) for a synthesis of this research.

The classic theoretical framework for such games was laid out in the "cheap-talk" sender-receiver game by[START_REF] Crawford | Strategic information transmission[END_REF].

Other studies focus on deception in a non strategic context. The most widespread task is the die-in-thecup game introduced by Fischbacher and Föllmi-Heusi (2013). When pay is related to performance and the latter cannot be observed, agents tend to exaggerate their performance, with signi…cant heterogeneity among them (a nonnegligible fraction faithfully reports poor performance).

See[START_REF] Frank | The ethics of competition[END_REF] for a clear account of why this view is too narrow.

Some lab experiments show that students in economics tend to be less cooperative in prisoners'dilemma(Frank et al. 1993(Frank et al. , 1996)).

See also[START_REF] Mccabe | Cheating among business students: A challenge for business leaders and educators[END_REF] reporting a higher self-reported propensity to engage in ethical misconduct

See the surveys byRosembaum et al. (2014),Jacobsen et al. (2018),[START_REF] Abeler | Preferences for truthtelling[END_REF] and the meta-analysis by[START_REF] Gerlach | The truth about lies: A meta-analysis on dishonest behavior[END_REF]. As a caveat, in the experiments by[START_REF] Barcelo | On the heterogeneity of people's (dis)honest behavior along two dimensions: Cost of lying and cost of acquiring information[END_REF] andGneezy et al. (2019), the proportion of liars who chose the extreme lie is nonetheless very large.

Altruism tempers overprovision under FFS and fosters undeprovision under CAP beyond what pure pro…t maximization would suggest.

See also[START_REF] Iezzoni | Survey shows that at least some physicians are not always open or honest with patients[END_REF].

0 The …rst study used a sample of students in economics, and the second study used an Internet sample of the US general population.1 1[START_REF] Vranceanu | Deceitful communication in a senderreceiver experiment: Does everyone have a price?[END_REF] found no correlation between lying aversion and inequality aversion.

2[START_REF] Erat | White lies[END_REF] implemented both a between-subject and a within-subject design. Our design combines within-subjects and between-groups comparisons.

3 In the instructions, T[1,10] and T[10,10] were inverted, exactly as they were presented in[START_REF] Erat | White lies[END_REF]. We reverse the labels to follow the intuitive order in which the payo¤ for the sender is increasing at constant payo¤ for the receiver.

4 The debate on the best method of eliciting risk aversion far is from settled. Di¤erent incentivized methods provide uncorrelated measures and are relatively unstable over time (seeCrosetto and Filippin,

2016;Beauchamp et al. 2016; Mata et al., 2019). Self-reported measures such as the scale introduced by[START_REF] Dohmen | Individual risk attitudes: Measurement, determinants, and behavioral consequences[END_REF] are less prone to such shortcomings but have limitations speci…c to unincentivized measures.1 5 The donation went to the UNICEF.

6 If no indication is provided, in this text, p-values correspond to two-sided t-tests.

7 In OLS regressions, coe¢ cients can be interpreted directly as changes in the probability of stating a lie. Unreported probit models provide very similar results.

0 Segmentation criteria are age, gender, socioprofessional category, type of residency and region. The survey is administered by computer-assisted web interviews.

Acknowledgement 1 This research was funded by academic grants provided by the Direction de la Recherche, International, Valorization et Ecoles doctorales (DRIVE) of the University of Paris Descartes and the LABEX MME DII of the University of Cergy Pontoise. It bene…ted from the agreement of the Ethical Committee of University of Paris Descartes on April 18, 2019. The authors are grateful to Delphine Dubart, at the ESSEC Experimental Lab, for her technical assistance, as well to Thierry Aimar, Nathalie Charnaux, Cécile Badoual, Jeanne Bregier, Philippe Henry, Fabrice Jollant, Marie-France Mamzer, Sophie Ng Wing Tin, and Jean Ralph Zahar for their support during the di¤ erent implementation stages of the experiment. They would like to thank Angela Sutan and Eli Spiegelman for their suggestions and remarks on an early version of the paper.

"You consider an exchange of information between a person who sends a message and a person who receives it. In this exchange, the sender of the message can either tell the truth, i.e., convey exact information, or lie, i.e., convey false information. Academic research has de…ned two types of important lies: a "black lie", which entails positive consequences for the liar and negative consequences for the receiver of the misleading message; these lies are bene…cial to the liar at the expense of the receiver; and a "white lie", which brings a bene…t to the person who receives it, and is costly to the person who tells it.

Please indicate whether you agree or disagree with the following four statements:

S1. An undergraduate student in medicine is more prone to tell black lies than an undergraduate student in business administration S2. An undergraduate student in medicine is more prone to tell white lies than an undergraduate student in business administration S3. In general, the use of black lies is more frequent in the business world than in the the medical world S4. In general, the use of white lies is more frequent in the business world than in the medical world

The answers were recorded on a seven-item scale, from 1 (full disagreement) to 7 (full agreement), 4 being the neutral case.

The …rst two items (S1 and S2) are directly related to the experiment. They aim to gauge how the general population perceives the lying behavior of the two groups of students.

Items 3 and 4 aim to capture the general opinion on deception within the business profession and the medical profession.

In the implementation of the survey, items 1 and 2 were alternated, as were items 3 and 4. The results of the survey Detail of the answers (all the 7 categories) to the survey on the representative sample of the French population (N=1035).

A Appendix

S1. An undergraduate student in medicine is more prone to tell black lies compared to an undergraduate student in business administration

S2. An undergraduate student in medicine is more prone to tell white lies compared to an undergraduate student in business administration S3. In general, the use of black lies is a more frequent practice in the business world compared to the medical world S4. In general, the use of white lies is a more frequent practice in the business world compared to the medical world If he or she chooses a number di¤erent than the actual outcome, you will receive $21 and he or she will receive $30

The message I will send in this payment option is "The outcome from the roll of the 6-sided die is ______."

(Please …ll in a number from 1 to 6.)

Payment possibility #3

If he or she chooses the actual outcome of the roll of the dice, two, then you will receive $20 and he or she will receive $20.

If he or she chooses a number di¤erent than the actual outcome, you will receive $30 and he or she will receive $30.

The message I will send in this payment option is "The outcome from the roll of the 6-sided die is ______."

(Please …ll in a number from 1 to 6.)

Payment possibility #4

If he or she chooses the actual outcome of the roll of the dice, 2, then you will receive $20 and he or she will receive $20.

If he or she chooses a number di¤erent than the actual outcome, you will receive $21 and he or she will receive $15.

The message I will send in this payment option is "The outcome from the roll of the 6-sided die is ______."

(Please …ll in a number from 1 to 6.)

Payment possibility #5

If he or she chooses the actual outcome of the roll of the dice, 2, then you will receive $20 and he or she will receive $20.

Please circle the amount you want to give: 0 1 2 3 4 5 6 7 8 9 10 euros.

C O N T A C T :

RESEARCH CENTER research@essec.edu