غبار کلاه برداری- کاهش پدیده کلاه برداری با ابهام استراتژیک

Most insurance companies publish few data on the occurrence and detection of insurance fraud. This stands in contrast to the previous literature on costly state verification, which has shown that it is optimal to commit to an auditing strategy. The credible announcement of thoroughly auditing claim reports is a powerful deterrent. Yet, we show that uncertainty about fraud detection can be an effective strategy to deter ambiguity-averse agents from reporting false insurance claims. If, in addition, the auditing costs of the insurers are heterogeneous, it can be optimal not to commit, because committing to a fraud-detection strategy eliminates the ambiguity about auditing. Thus, strategic ambiguity can be an equilibrium outcome in the market. Even competition does not force firms to provide the relevant information. This finding is also relevant in other auditing settings, like tax enforcement.

Fraudulent claims on insurance policies are an important issue for insurers. The extent of insurance fraud varies widely from small overstatements of claims to deliberately pretending damages that never occurred or that were intentionally arranged. Due to the nature of fraud, estimating the losses for the insurance industry is not an easy task. Nevertheless, the Insurance Information Institute, for example, estimates that in both 2004 and 2005 insurance fraud amounted to $30 billion in the U.S. property and casualty insurance market.1 This number is consistent with the estimate of $20 billion for 1994 by the National Insurance Crime Bureau as stated in Brockett et al. (1998). According to Caron and Dionne (1997), 10% of insurance claims in the automobile insurance are fraudulent to some extent in the Canadian province of Quebec. Therefore insurersʼ strategies to deter insurance fraud do matter. Dionne et al. (2009, p. 69), for example, estimate that in their sample, companies could save up to 41% of the costs due to fraudulent claims by implementing the optimal auditing strategy. Such a strategy has to balance auditing costs and benefits, like exposed fraudulent claims. In the mass market and with small claims, it is too costly to audit each claim that is made. Consequently, claim reports are usually scanned for known patterns of fraud and only a certain fraction of these reports is verified in detail. Previous literature, like Picard (1996), who analyzes the canonical model of insurance fraud, suggests a commitment problem. Ex ante insurers are interested in announcing a high level of auditing to deter insurance fraud. Given the announced level of auditing, policyholders indeed report only few fraudulent claims. As auditing is costly, however, insurers have an incentive to audit only very few claims ex post, rendering their ex-ante announcement not credible. Credible commitment to a certain level of auditing solves this dilemma. Thus, the absence of commitment implies a welfare loss. In contrast to this theoretical result, empirically it is very unusual for insurers to make their level of auditing publicly available. There are also no observable efforts to overcome the credibility issue by having an industry association scrutinize their level of auditing or using another third-party verification mechanism. Insurance firms not only announce no data on fraud detection and auditing, but even block access to it. Thus, there are very few empirical studies available.2 This behavior indicates that conventional wisdom neglects some aspects of the setting. Therefore we suggest that there is an additional issue. We depart from previous literature by assuming ambiguity-averse policyholders and uncertainty about insurersʼ costs of an audit.3 We model the ambiguity on the type space, as the insured do not know which type of insurer they are facing. This leads to ambiguity about the probability of an audit. In our model, ambiguity-averse agents undertake less fraud due to this uncertainty. Yet commitment dissolves this ambiguity as it makes the level of auditing common information. We show that, even in a competitive market, it can be optimal for insurers to maintain the ambiguity and forgo commitment.4 Thus, strategic ambiguity is an equilibrium outcome.5 First, we prove that holding insurersʼ behavior fixed, ambiguity makes fraud less appealing. Next, we endogenize the insurersʼ behavior. In the second step, we show that for a given contract, if the insurer abstains from commitment, ambiguity aversion either lowers the amount of fraud while holding the level of auditing fixed, or vice versa. Third, we prove that avoiding commitment is optimal if the auditing costs satisfy certain conditions discussed in the next paragraph. Finally, we also endogenize contracts. The utility-maximizing contract that just breaks even under no commitment can be the unique equilibrium outcome. Insurance companies have different reasons to forgo commitment. Insurance companies with high costs save on auditing costs, if they hide their type by abstaining from commitment, because the average auditing probability is higher than their own. Insurance companies with low costs also prefer the uncertainty to commitment, because a higher level of fraud due to the lower average auditing makes their auditing even more profitable. This is caused by the improved ratio between their low costs and recovered indemnities and fines imposed on uncovered fraudsters. Risk aversion leads to different effects in model than ambiguity aversion. If the degree of risk aversion increases, the deterrence of insurance fraud becomes easier both with and in the absence of commitment. Ambiguity aversion has only deterrence effects if there is no commitment. Therefore, only ambiguity aversion influences the balance between commitment and non-commitment. After all, it is the uncertainty that makes ambiguity-averse agents less inclined to engage in insurance fraud.6 In our model, policyholders are ambiguity-averse. Ambiguity denotes uncertainty about probabilities resulting from missing relevant information. We therefore distinguish ambiguity and risk.7 In the absence of ambiguity, there is a known probability distribution, while under ambiguity the exact probabilities are unknown. Savage (1954) and Schmeidler (1989) have developed two axiomatized approaches to this problem. Subjective Expected Utility of Savage requires the decision maker to be ambiguity-neutral. This approach has been criticized for various reasons. From a normative point of view, it seems appropriate to take into account the amount of information on which a decision is based. This point was first made by Ellsberg (1961). In addition, there are empirical observations, like Kunreuther et al. (1995) or Cabantous (2007), which suggest that the Subjective Expected Utility approach neglects the distinction between risk and ambiguity. Insurers, which face ambiguity, usually request higher premiums and reject to offer an insurance policy in more cases than in the absence of ambiguity. The model in our paper uses the representations of preferences with ambiguity aversion by Klibanoff et al. (2005) and Gilboa and Schmeidler (1989). In both representations, the decision maker judges situations with missing information more pessimistically than an ambiguity-neutral individual. The problem of costly state verification considered here is not limited to insurance fraud, but also appears in different settings such as financing (Gale and Hellwig, 1985), accounting (Border and Sobel, 1987), principal–agent relationships (Strausz, 1997) or enforcement of TV license fees (Rincke and Traxler, 2011). The main point is that there is often asymmetric information between the parties to a contract. To avoid the exploitation of these asymmetries, the uninformed side has to use costly state verification technologies, like ticket inspections in public transport. Townsend (1979) began this analysis of the trade-off between auditing costs and losses due to the remaining information asymmetries. Commitment is optimal in these models, as discussed in, e.g., Baron and Besanko (1984). Hence, there have been various proposals to make commitment feasible and credible. Melumad and Mookherjee (1989) introduce delegation as a commitment device and Picard (1996) proposes a common agency financed by lump-sum payments to subsidize auditing costs. This lowers the variable costs of auditing claims in order to solve the credibility problem. Yet we will argue in this paper that in some circumstances it is optimal for firms to avoid commitment to an auditing strategy, even if commitment were possible and costless. Previous literature that combines costly state verification and uncertainty about auditing costs often uses a setting of tax evasion. Cronshaw and Alm (1995) analyze this case, but without ambiguity aversion and without the possibility of commitment. Therefore, in their model, uncertainty could be counterproductive. Snow and Warren (2005), on the other hand, model ambiguity aversion by a subjective weighting of probabilities. Their paper studies the behavior of taxpayers given this ambiguity, but there is no possibility of commitment. Thus, our paper is the first to consider the strategic decision of commitment versus uncertainty. The notion of strategic ambiguity as the strategic choice to withhold information in order to maintain the uncertainty for the other contract party has been used by Bernheim and Whinston (1998) and Baliga and Sjöström (2008) in the context of ambiguity-neutral players. In Baliga and Sjöström (2008), a country in equilibrium withholds the information about its military arsenal instead of acquiring arms with certainty and uses strategic ambiguity as a substitute for arms acquisition. In Bernheim and Whinston (1998), on the other hand, strategic ambiguity denotes the choice of an incomplete contract. Bernheim and Whinston (1998, p. 920) show “that, when some aspects of behavior are observable but not verifiable, it may be optimal to write a contract that leaves other potentially contractible aspects of the relationship unspecified.” The assumption of observable, but unverifiable aspects, while common in this literature, does not apply here. Individual fraud is either unobservable and unverifiable without an audit or becomes verifiable after an audit. Aggregate fraud levels are unobservable for policyholders and in reality for insurers, too. The type of an insurer is unobservable for the insured, while the occurrence of an audit is verifiable. Therefore there is no scope for negotiations that could make incomplete contracts optimal. Instead it is one party, the insurer, who decides to withhold the information about its auditing probability at a later stage after the contracting. The optimality of incomplete contracts is confirmed by Mukerji (1998) for ambiguity-averse parties. In his paper, contractual incompleteness lessens the effects of ambiguity, because it leads to renegotiations that yield a proportional split of the surplus. This reduces the utility losses due to ambiguity, as it makes the considerations of both parties how to determine the worst distribution more similar.8 In our model, avoiding commitment enhances the effects of ambiguity.9 A second contribution of this paper is to scrutinize a model with ambiguity aversion in a game-theoretic framework. Although many papers deal with the effects of ambiguity aversion in decision making and finance, there are few papers on games with ambiguity-averse players.10 The reasons are problems with the equilibrium concepts, as addressed by Dow and Werlang (1994), Klibanoff (1996), Lo, 1996, Lo, 1999 and Lo, 2009, Marinacci (2000), Eichberger and Kelsey (2000), Bade (2011a), and Riedel and Sass (2011). We avoid these problems by modeling the ambiguity on the type space, i.e., the auditing costs of the insurers. This approach is also used by Lo (1998), Levin and Ozdenoren (2004), Bose et al. (2006), and Bodoh-Creed (2012) to study auctions with ambiguity-averse bidders. Bade (2011b) uses this approach, too, in order to establish the existence of equilibria in games of multidimensional political competition. It allows using common equilibrium concepts, like perfect Bayesian equilibrium. The third contribution is to consider whether competition makes firms provide relevant information to consumers and educate them. The argument by, e.g., Laibson and Yariv (2007) has been that competitive pressure gives consumers all the relevant information, as a competitor could always reveal the information and win market share. In our model, this is not the case. There is a market equilibrium with perfect competition where firms do not announce their information about auditing levels and ambiguity prevails that allows mitigating the effects of insurance fraud. In this respect, our results are similar to Gabaix and Laibson (2006) and Heidhues et al. (2012), where in equilibrium firms shroud the prices of some add-ons to their products. The remainder of the article is organized as follows. Section 2 sets up a stylized model to give an intuition as to how ambiguity about the level of auditing decreases insurance fraud. In addition, it explains the decision process of the ambiguity-averse policyholders. In Section 3, we take contracts as given and insurers decide on their auditing probabilities and whether or not to commit to their fraud-detection strategy. We show that commitment can decrease profits and that insurers do not want to commit, even if they have the possibility to do so. In Section 4, insurers compete in contracts and decide on their auditing strategies. Even in this competitive market, firms in some cases want to forgo commitment. Then Section 5 compares the effects of ambiguity aversion with risk aversion. Finally, Section 6 exploits some extensions of the model and Section 7 contains the concluding remarks.

In this paper, we discuss a costly state verification model with ambiguity about auditing costs. For this purpose, we use an insurance fraud setting. We show that ambiguity aversion reduces the inclination to engage in insurance fraud at a given level of auditing. Insurers, on the other hand, can gain by not committing to an auditing probability and maintaining the uncertainty, even if this means abandoning the advantages of commitment. Hence, in the main contribution of this paper we prove that uncertainty can be a feasible deterrence device. The second contribution is to study a model with ambiguity aversion in a game-theoretic framework. Although ambiguity seems even more relevant in a strategic interaction than for a single player, the literature on ambiguity aversion has so far focused on decision theory and finance with notable exceptions discussed in the introduction. We provide a game-theoretic analysis of ambiguity-averse policyholders. Modeling the ambiguity on the type space, i.e., the auditing costs of the insurers, allows the use of common equilibrium concepts. The third contribution of this paper is to consider whether competition forces firms to educate consumers. According to a common line of argument, competitive pressure provides consumers with all relevant information, as competitors have an incentive to reveal the information in order to increase their market shares. In our model, uncertainty prevails and on the equilibrium path no firm has an incentive to make auditing costs or probabilities public. Therefore, there is a market equilibrium with perfect competition where firms do not grant access to their information about auditing probabilities and costs. The resulting uncertainty allows mitigating the effects of insurance fraud. Finally, we summarize the incentives of insurers to avoid commitment. Insurers benefit from policyholdersʼ aversion to the ambiguity about the auditing and the resulting lower level of fraud if their costs of auditing are high enough. For low costs, however, insurers gain from non-committing, as they catch more fraudsters, thus saving indemnities and earning fines at low costs. In some cases, these effects are so strong that the costs caused by fraud and its deterrence are lower than under credible commitment to an auditing level. Consequently, insurers opt to implement strategic ambiguity.