جرائم، هماهنگی، و مجازات: یک تجزیه و تحلیل اقتصادی

In the standard economic theory of crime and punishment, a risk-neutral individual will commit an offense if and only if his private benefit exceeds the expected sanction for doing so. To the extent that several individuals simultaneously choose whether or not to commit the offense, it is assumed that their decisions are independent of each other. The purpose of this paper is to investigate a situation in which an individual’s propensity to engage in an illegal activity may depend also on the behavior of other individuals. We consider a two-period model: In each period, individuals decide simultaneously whether to commit the offense. A police authority is in charge for the arrest and conviction of offenders. We assume that the police authority has a limited enforcement budget such that it cannot arrest and convict every offender. In this situation, the expected payoff of an individual from committing the offense is higher the more individuals also decide to behave illegally. We analyse the interactive behavior in this model and answer the following questions: When are individuals responding to others’ behavior, when are they influencing others’ behavior. And, what is the optimal enforcement policy to forestall interactive behavior.

In Basel, Switzerland, handicrafts are traditionally organized in guilds. Besides representing the interests of their members, the main purpose of guilds is to share business information and to cultivate commercial relations. Commenting on enforcement of environmental regulations, representatives of the environmental agencies in Basel remarked that meetings by guild members are also used to exchange information concerning individual compliance with law. They expect that such information about the behavior of other members influences the propensity of one member to comply with environmental regulations. The reason for this apprehension is well justified: To induce as many firms as possible to engage in adequate protection, the environmental agencies used a sequential enforcement process—see for example Shavell [1991] or Mookherjee and Png [1992]: First, they make spot inspections (general enforcement) which keeps enforcement costs low, but implies that monitoring will be imprecise. If a monitoring visit indicates insufficient protection, an agency investigates in a second step the actual degree of the firm’s protection at high cost (specific enforcement). Now suppose that the owner of an environmentally risky plant knows that others are already violating environmental regulations. Since a limited enforcement budget restricts the agency’s ability to detect all violations, the agency has to concentrate its specific enforcement activities to only some of those firms where general enforcement indicated an offense. But then the incentive of the owner to behave illegally increases with the number of firms already violating the regulations because the probability that the agency actually investigates his plant decreases. One of the most important issue confronted by environmental agents thus is to organize their enforcement activities to forestall such interactive behavior. The standard literature on crime and punishment fails to give a suitable theoretical answer to this issue. According to Becker’s [1968] seminal study, a risk-neutral individual will commit an offense if and only if his private benefit exceeds the expected sanction for doing so.1 To the extent that several individuals simultaneously choose whether or not to commit the offense, it is assumed that their decisions are independent of each other. An individual’s compliance decision then is not influenced by the behavior of other individuals. The behavior of the aggregate is merely an extrapolation from the behavior of an individual. Situations, however, in which an individual’s behavior depends on what others are doing usually do not permit simple extrapolation of individual behavior to the aggregate.2 To make that connection we then have to look at the system of interaction between individuals: When do individuals respond to others’ behavior; when do they influence others’ behavior; and (in case of criminal activities) what is the optimal enforcement policy to forestall interactive behavior? The purpose of this paper is to investigate these questions in a game-theoretical model.3 There are two risk-neutral individuals. Each individual knows his own private benefit from committing an offense, but not the other individual’s payoff. The timing of the game has two periods. In each period, individuals decide simultaneously whether to commit the offense. An offender is subject to a sanction when he is caught. Before his second period decision, an individual observes the first period behavior of the other individual. A police authority is in charge of the arrest and conviction of offenders in both periods. We assume that the police authority has a limited enforcement budget such that it cannot arrest and convict every offender per period.4 In this situation, interactive behavior emerges because the expected sanction for an offender if both individuals commit the offense is lower than the expected sanction if only one individual commits the offense. As a result, the expected payoff to an individual from committing the offense is higher the more likely it is that the other individual is also an offender.5 The first issue with interactive behavior in our model lies on the supply side of offenses. Because of their interdependent payoff functions, an individual must anticipate the behavior of the other. In the two period model, an individual will use the first period behavior of the other individual as a signal of his propensity to engage in the illegal activity at date two. Of course, to be (or not to be) an offender in period one is not a commitment to future behavior. This introduces coordination problems. Since both individuals prefer to coordinate their decision to commit the offense, the following two behavior patterns may arise: In case of active coordination, an individual commits the offense at date one in order to demonstrate high private benefits but switches to legal behavior at date two if the other individual behaved legally at date one. And, in case of passive coordination, an individual behaves legally at date one and switches to illegal behavior at date two if the other individual committed the offense at date one. The second issue relates to the demand side of offenses, i.e. the way police authority should allocate resources for policing between the two periods. The way in which police resources are allocated influences the possibility for interactive behavior of individuals and therefore the overall crime rate. We assume that the authority’s objective is to minimize the total number of offenses in both periods.6 To this purpose, it will try to reduce possible coordination between individuals. In Section 2 we introduce into the basic one-period model. In the next two sections we analyze the two-period model. First, in Section 3, we consider the case in which the police authority has a fixed identical budget for each period. This case captures the features of many enforcement problems in reality and focuses only on interactive behavior under a given institutional framework. Second, in Section 4, we analyze the general case in which the police authority has the possibility to shift part of its budget from one period into another period.7 We characterize individuals’ behavior for any given allocation of resources and then show how the authority should allocate resources optimally in order to minimize the expected number of offenses. Section 5 concludes with some final remarks.

5. Conclusion and extensions In this article we have analyzed decision-interdependency among potential offenders and characterized the optimal enforcement policy to forestall interactive behavior. We have shown that it is optimal for a police authority to concentrate police actions in order to minimize coordination between individuals. To the extent that there are more than two periods, this result suggests that it is optimal for the police authority to use the following strategy: concentrate resources in period 1 to forestall criminal behavior, and do so in all subsequent periods as long as the budget allows. This, of course, is a well known strategy in real law enforcement situations. For example, local transport companies often use surprise controls with several ticket inspectors to avoid interactive travelling without a ticket. Our result could also be extended to different types of offenses.14 Suppose for example that there are two types of offenses and that the police authority has a limited budget to enforce both offenses. If the authority is free to allocate its resources, our results suggest the following optimal policing strategy: concentrate police actions on one type of offense in period 1 and on the other type of offense in period 2. If, however, the police authority is restricted in its allocation of resources, conditional policing in period 2 is optimal: shift as many resources as possible to the enforcement of that offense, that is most prevalent in period 1. We assumed throughout the paper that the police authority can commit itself to a certain policy. Therefore, individuals (when deciding on whether to commit the offense) can condition their behavior on this information. Although this is a standard assumption in the theory of crime and punishment (see Besanko and Spulber [1989] for an exception), it would be of interest to consider a situation in which the police authority decides on policing simultaneously with the individuals’ decisions. The literature on tax evasion suggests that the optimal policing crucially differs from the one derived here, see e.g. Reinganum and Wilde 1985 and Reinganum and Wilde 1986]. In particular, if the tax authority cannot commit itself to its auditing policy, it faces the following credibility problem: Suppose that from an ex-ante perspective, the tax authority prefers to audit with positive probability, thus providing appropriate incentives for truthfully given tax reports. However, if the taxpayers behave as supposed, the tax authority might not have an ex-post incentive to audit, for it can save on costs. Of course, his behavior will be foreseen by the taxpayers and the authority’s ex-ante announcement to audit will not be credibly ex-post. Thus, the tax authority has to rearrange the tax system in such a way that his threat to audit becomes credible at the time of performance.15 The model could also be extended to consider the case in which the authority is required partially to self-finance by retaining a share of the sanctions it collects. Further work should also consider more than two individuals. The mechanism discussed here may then serve as an explanation of the formation of riots and mobs.