metadata: authors: 0: author: Basu, Karna
1: author: Basu, Kaushik
2: author: Cordella, Tito
count: World
docna: 0: docna: Asymmetric punishment as an instrument of
            corruption control
docty: Policy Research Working Paper
subtopic: Social Policy,Legal Products,Law Enforcement Systems,Judicial System Reform,National Governance,Government Policies,Urban Solid Waste Management,Public Sector Economics,Youth and Governance,Legal Reform,Legislation,Regulatory Regimes,Public Finance Decentralization and
            Poverty Reduction,Global Environment,Crime and Society
teratopic: Law and Development,Public Sector Development,Social Development,Private Sector Development
abstracts: cdata!: The control of bribery is a policy
            objective in many developing countries. It has been argued
            that asymmetric punishments could reduce bribery by
            incentivizing whistle-blowing. This paper investigates the
            role played by asymmetric punishment in a setting where
            bribe size is determined by Nash bargaining, detection is
            costly, and detection rates are set endogenously. First,
            when detection rates are fixed, the symmetry properties of
            punishment are irrelevant to bribery. Bribery disappears if
            expected penalties are sufficiently high; otherwise, bribe
            sizes rise as expected penalties rise. Second, when
            detection rates are determined by the bribe-giver, a switch
            from symmetric to asymmetric punishment either eliminates
            bribery or allows it to persist with larger bribe sizes.
            Furthermore, when bribery persists, multiple bribe sizes
            could survive in equilibrium. The paper derives parameter
            values under which each of these outcomes occurs and
            discusses how these could be interpreted in the context of
            existing institutions.
repnme: repnme: Asymmetric punishment as an instrument of
            corruption control
display_title: Asymmetric punishment as an
            instrument of corruption control
listing_relative_url: /research/2014/06/19705390/asymmetric-punishment-instrument-corruption-control
topicv3: Anti-Corruption m1326754 832,Law Enforcement m1326759 2082,Organized Crime m1327084 2453,Environment, Natural Resources and Blue
            Economy m1327391 566,Crime m1439217 3041
publishtoextweb_dt: 2014-06-01T00:00:00Z
historic_topic: Law and Development,Public Sector Development,Social Development,Private Sector Development
no_of_pages: 21
model_extractions: WPS6933 Policy Research Working Paper 6933 Asymmetric Punishment as an Instrument of Corruption Control _Karna Basu Kaushik Basu Tito Cordella_ The World Bank Development Economics Vice Presidency Office of the Chief Economist June 2014
Policy Research Working Paper 6933

# **Abstract**

The control of bribery is a policy objective in many developing countries. It has been argued that asymmetric punishments could reduce bribery by incentivizing whistle-blowing. This paper investigates the role played by asymmetric punishment in a setting where bribe size is determined by Nash bargaining, detection is costly, and detection rates are set endogenously. First, when detection rates are fixed, the symmetry properties of punishment are irrelevant to bribery. Bribery disappears if expected penalties are sufficiently high; otherwise, bribe sizes rise as expected penalties rise. Second, when detection rates are determined by the bribe-giver, a switch from symmetric to asymmetric punishment either eliminates bribery or allows it to persist with larger bribe sizes. Furthermore, when bribery persists, multiple bribe sizes could survive in equilibrium. The paper derives parameter values under which each of these outcomes occurs and discusses how these could be interpreted in the context of existing institutions.

This paper is a product of the Office of the Chief Economist, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at kbasu@hunter.cuny.edu, kbasu@worldbank.org, and tcordella@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Asymmetric Punishment as an Instrument of Corruption Control<sup>∗</sup>

Karna Basu,<sup>†</sup> Kaushik Basu<sup>‡</sup> and Tito Cordella<sup>§</sup>

> ∗This paper has benefited from conversations with Christian Ahlin, Jonathan Conning, Avinash Dixit, Aristomene Varoudakis, and seminar participants at the University of Pennsylvania Law School.

> †Hunter College, City University of New York; E-Mail: kbasu@hunter.cuny.edu

> ‡The World Bank, 1818 H St. NW, Washington, DC 20433, USA; E-Mail: kbasu@worldbank.org

> §The World Bank, 1818 H St. NW, Washington, DC 20433, USA; E-Mail: tcordella@worldbank.org.
# 1 Introduction

Corruption is a major concern in several countries. One reason it is diffi cult to control is that those involved have an incentive to collude to prevent detection. While this is a feature of many criminal activities, the problem under corruption is heightened by criminal codes that, in most countries, penalize the bribe-giver and the bribe-taker equally.<sup>1</sup> As a result, all participants in a bribing scheme, including those who might otherwise be considered victims and could be tempted to act as whistle-blowers, have a vested interest against doing so.

How could such collusion be weakened and bribery reduced? A possible solution that we discuss in this paper lies in asymmetric punishments. The basic justification for asymmetric punishments is that, by penalizing some parties less than others, the government can create ex-post incentives for agents to report the crime and thereby stop colluding.

The idea of asymmetric punishment for crime is not new and it has been implemented in various forms around the world. For example, prosecutors in the United States sometimes offer immunity to those who reveal financial crimes that they might themselves have been complicit in. In Italy, similar schemes have been used to fight organized crime.

If asymmetric punishment is quite widespread in the case of financial and organized crime, it is relatively rare in the case of bribery.<sup>2</sup> This is somewhat surprising, especially in the context of harassment bribes where (i) citizens are asked to pay a bureaucrat to receive services that they are legally entitled to, and (ii) the bribe does not itself change the nature of the services being exchanged.<sup>3</sup> Harassment bribes are pervasive in developing countries (and sometimes beyond) and directly affect large segments of populations.<sup>4</sup> This means that there might be significant political returns to tackling such corruption with innovative solutions. In a note for India’s Ministry of Finance, one of us (Basu, 2011) proposed the following: decriminalize the giving (but not taking) of harassment bribes and require the bribe-taker to return the bribe to the citizen if caught.<sup>5</sup> This would create ex-post incentives for citizens to reveal that bribes were paid, and could end up discouraging bureaucrats from demanding bribes in the first place.

Inspired by the animated discussion that followed this proposal,<sup>6</sup> and to

> 1 See Linklaters (2012) for a survey.

> 2 There are some exceptions, discussed in Li (2012) and Engel et al (2012).

> 3 As would be the case if, for example, an entrepreneur were paying a bribe to avoid complying with environmental standards.

> 4 While not relevant to this paper, the distinction between harassment bribes (a type of extortion) and other forms of bribery is a complex one. See, for example, Carson (1985) and Oak (2013).

> 5 According to India’s Prevention of Corruption Act (1988), the giver and the taker of a bribe are considered equally culpable and can be financially penalized and incarcerated for up to five years.

> 6 The proposal led to a large controversy with questions being raised by members of the Indian Parliament. It received wide publicity in the print and electronic media. See, for instance, The Economist (2011), Dreze (2011), Sainath (2011), Mitra (2011), Seabright (2011), Haider (2012), and Zakaria (2011).

2
assess its “robustness”, in this paper we study how different punishment schemes are likely to affect the size and incidence of harassment bribes. This allows us to shed some new light on the conditions under which asymmetric punishment is able to deter bribe-giving effectively.

We develop a simple model in which a bureaucrat can costlessly provide a service that creates a surplus for the citizen, but might demand a bribe in exchange. If a bribe is demanded, the bureaucrat and the citizen split the surplus through a process of Nash bargaining.

We first analyze a benchmark case where the fines for bribe-giving and bribetaking and the probability of detection are exogenous. In such a setting, a bribe is exchanged as long as the total expected penalty is small enough. Interestingly, the symmetry properties of the punishments are irrelevant to the incidence of bribery. Whether the penalty burden falls disproportionately on the bureaucrat or the citizen, and whether the bureaucrat is required to repay part of the bribe, do not matter: the bribe size will adjust to keep the surplus equally split.

Furthermore, we show that bribe sizes could rise when anti-corruption enforcement is strengthened. Intuitively, if penalties are at all asymmetric, as enforcement improves the citizen must pay a larger bribe to compensate the bureaucrat for his relatively larger expected penalty. This means that if bribery is measured by bribe size, an attempt to reduce bribery might instead increase it.

Next, we relax the assumption that the probability of detection is exogenous, and we assume that it depends on costly actions undertaken by the state and/or the citizen. We show that asymmetric punishment increases the incentives for the citizen to whistle-blow. However, whether this leads to the elimination of bribery, as in Basu (2011), or to an exacerbation of the problem—in which bribery persists and the bribe size rises to account for the greater probability of detection—depends on the effectiveness of law enforcement agencies in detecting corruption. Asymmetric punishments could also give rise to multiple equilibria with two possible outcomes—one where the bribe size is small and the probability of detection is also small, and another where both the bribe size and probability of detection are large.

This necessarily complicates policy prescriptions. If it is suffi ciently easy for a citizen to get the corrupt bureaucrat caught, asymmetric punishment can be an effective tool to eliminate bribery. However, in countries where the marginal cost of improved detection is high, possibly the same countries where harassment bribes are a problem in the first place, bribery will survive under asymmetric punishment. When this is the case, bribe size might rise to account for the fact that the offi cial is more likely to be penalized due to the entrepreneur’s efforts to report. Here, asymmetric punishment in fact creates an effi ciency loss through the costs associated with whistle-blowing. Our model could therefore partly explain why a country like China, which implemented asymmetric punishments in 1997 but has high costs of reporting, has not experienced a discernible reduction in corruption (Li, 2012).

Bribery and corruption have been subjects of economic inquiry for some time (see Bardhan, 1997, for a comprehensive survey). In their seminal paper, Shleifer 3
and Vishny (1993) show how institutions affect the prevalence and effi ciency implications of corruption. More recently, several papers present theoretical analyses of approaches to reduce corruption (see, among others, Andrianova and Melissas, 2008 and Dixit, 2013). The present paper belongs to that tradition and relates closely to the growing academic literature on the possibilities and limitations of asymmetric punishment (see Rose-Ackerman, 1999; Lambsdorff and Nell, 2007; and Oak, 2013). On this topic, Rose-Ackerman (2010) and Dufwenberg and Spagnolo (2013) are particularly relevant to our analysis.

The first paper, which is a critical survey of the law and economics of bribery and extortion, provides a wide-ranging discussion of how different punishment schemes affect the bargaining between the bribe-giver and bribe-taker. While some of the intuition of our paper can be found there, our contribution lies in the formalization of the analysis and the endogenization of costly actions undertaken by the bribe-giver.

Dufwenberg and Spagnolo (2013) provide a rigorous game theoretic formulation of Basu’s (2011) proposal. In a non-cooperative framework, they show that, in a one shot game, asymmetric punishment either has no effect or prevents bribery but at the cost of the service offered. Which of these is realized depends on whether, in the absence of a bribe, institutions are effective enough to incentivize the bureaucrat to offer the service. They then consider a repeated version of the game in which the bureaucrat has an incentive to build a reputation of being corrupt. In such a set-up, they show that asymmetric punishment indeed becomes an effective instrument to fight corruption but only if institutions are good.

Our paper complements Dufwenberg and Spagnolo (2013) through the introduction of a new set of realistic and consequential considerations. By modeling the interaction between the bureaucrat and citizen as a bargaining game, we endogenize bribe size, making it a function of the punishment regime as well as the probability of detection. In addition, by endogenizing probabilistic detection we generate some nuanced results including the possibility that asymmetric punishment could raise bribe size.

Aside from the theoretical research, there is a limited but growing empirical literature on the effectiveness of asymmetric punishment in deterring harassment bribes. On the one hand, Abbink et al. (2014) provide some experimental evidence supporting the use of asymmetric punishment. On the other, Engel et al. (2013) use a lab experiment to show that, when the bureaucrat can bestow favors in response to a bribe, asymmetric punishment raises the incidence of bribery. Additional empirical work, guided by economic theory, can continue to refine our understanding of how alternative forms of punishment may affect incentives to demand and pay bribes.

Our goal is to bring some carefully constructed game theoretic methods to investigate a subject of great practical significance and vigorous public debate. Not surprisingly, the analysis does not lead to a unique prediction, but to conditional results which try to delineate where a certain kind of law will work and where it will not. Our model provides a stylized description of the mechanics that underlie bribery, and emphasizes the subtle interaction of two fundamental 4
choices—bribe size and detection probability. It is hoped that by bringing dispassionate analysis to bear on this emotive subject, we are able to shed some light on what is ultimately a practical matter of policy in law and economics.

# 2 Setup

## 2.1 Assumptions

Suppose an entrepreneur (denoted E) needs a licence to conduct his business. The license gives him a benefit of L > 0. The government offi cial (denoted O) is able to deliver the license costlessly. However, he considers the possibility of charging the entrepreneur for the license; that is to demand a bribe. Assume the offi cial has two choices—deliver the license for free, or make license delivery conditional on a bribe being paid. If he chooses the latter, he and the entrepreneur must bargain over the bribe size, and if they are unable to agree, no license is delivered.

Suppose the offi cial decides to demand a bribe. If a bribe size is agreed upon and paid, it is detected with probability p ∈ [0, 1]. If detected, the entrepreneur is penalized FE ≥ 0 and the offi cial is penalized FO ≥ 0. These penalties could constitute fines or other non-pecuniary costs. In addition, the offi cial is required to return a fraction β ∈ [0, 1] of the bribe paid. We define perfectly symmetric punishment as FE = FO and β = 0, and perfectly asymmetric punishment as FE = 0 and β = 1.

We shall throughout assume that the fine on the offi cial is at least as large as the fine on the entrepreneur: A1. FO ≥ FE.

In the case of harassment bribes this is a reasonable assumption and allows us to limit the cases we study without altering the qualitative conclusions of the analysis.

## 2.2 Bargaining

We use the standard Nash bargaining solution to determine the bribe size. For any bribe B ∈ [0, L], the entrepreneur’s utility is: Similarly, the offi cial’s utility is: If the players fail to agree on a bribe size, they both receive their outside options valued at 0.

If a solution exists, it is given by the following: 5
Since {(VE (B) , VO (B)) : B ∈ [0, L]} is a compact and convex set, a Nash bargaining solution exists as long as the penalties are suffi ciently small; that is, if there is some B<sup> ̃</sup> such that VE B ̃ , VO B ̃ ≥ (0, 0). We assume that the � � � � �� offi cial decides to demand a bribe if, and only if, a Nash bargaining solution exists (which, given the threat points, would automatically leave him weakly better off than not demanding a bribe).

Indeed, the exchange of a bribe comes closest to the kind of two-person negotiating situation that Nash (1950) had envisaged. Because of its illegal nature, there is seldom a third party or competitor involved during a transaction. It is a face-off between two individuals—a classic bargaining situation. While there are competing bargaining models, such as the one by Kalai and Smorodinsky (1975), which have the advantage of a slightly wider domain of application (see Anant, Mukherji, and Basu, 1990), in this case they are unlikely to make any substantial

# 3 Benchmark Model

Assuming a bribe is paid, the equilibrium bribe size is determined by: This yields the following bribe size: The corresponding utility is: First, let us analyze the utility from a bribe. The Nash bargaining solution leaves the players with identical utility—they essentially agree to split the gains generated by the license. Any rise in penalties results in a smaller surplus to be shared, so utility drops. Observe that the resulting utility is unaffected by β, the fraction that the offi cial must return if caught. Since β does not affect the total surplus to be shared, any redistribution that emerges from punishment is accounted for in the bribe size—a larger β results in a larger bribe size.

Next, we analyze equilibrium bribe size. We can see that a solution exists if and only if p (FO + FE) ≤ L. In other words, for a bribe to be exchanged, there must remain some surplus beyond the total expected punishment.

Equation 5 lends itself to some natural comparative statics analysis. In particular, we might be interested in how the punishments and especially their symmetry properties affect equilibrium outcomes. It can easily be verified that <u>∂B∂F0</u><sup>∗>0and</sup> ∂F<sup><u>∂B</u></sup> E<sup>∗<0.Intuitively,theonewhoexpectstogetpenalizedmore</sup> heavily needs to be given more up-front. Similarly, <u>∂B∂β</u><sup>∗</sup> > 0 — if the offi cial 6
expects to have to return some of the bribe, more needs to be paid. Finally, consider how B<sup>∗</sup> changes in response to p: The first and second derivatives are weakly positive if, and only if, FO − FE ≥ −βL. This means that the bribe size rises in p if the rise in p hurts the offi cial suffi ciently more than it hurts the entrepreneur. This condition is automatically satisfied by Assumption 1.

The results above are summarized in Proposition 1.

Proposition 1 Suppose FO, FE, β, and p are set by the government. (a) If p (FO + FE) > L, bribes are eliminated. (b) If p (FO + FE) ≤ L, a bribe is exchanged and the bribe size is strictly rising in FO, strictly dropping in FE, and strictly rising in β. Given A1, the bribe size is strictly rising in p except if FO = FE and β = 0, when it is constant in p.

Two important lessons emerge even from this simple setting. The first is that the symmetry properties of the punishment are irrelevant to the elimination of bribery. Bribery is eliminated as long as (FO + FE) is large enough. Whether the penalty burden is on the offi cial or the entrepreneur, and whether the offi cial is required to repay part of the bribe, do not matter, since the bribe size can adjust to account for them. To eliminate bribery, the state simply needs to drive up the expected total punishment high enough that the offi cial will not ask for a bribe. How it does so depends on its costs of adjusting p, FO, and FE. In the next section, we introduce a richer and arguably more realistic setting to further examine how asymmetric punishment might affect bribery.

The second lesson is that bribe sizes can rise when anti-corruption enforcement is strengthened. If bribery is measured by bribe size, an attempt to reduce bribery can instead increase it. In particular, if the penalty is low to begin with, a rise in the offi cial’s fine or in the detection probability will result in a larger bribe. Our point here is that a larger bribe should not be interpreted as more severe bribery—it is simply a reflection of the reallocation of surplus between entrepreneur and offi cial. Larger bribes seem to suggest a more acute problem, but policies designed to detect bribery might themselves raise the size of the bribe.

# 3.1 Bribe Size as a Function of Detection Probability

As Equations (5) and (7) show, B<sup>∗</sup> is rising in p. Figure 1 depicts B<sup>∗</sup> (p) for some relevant parameter values. As noted before, the incidence of bribery is unaffected by the symmetry properties of punishment. However, bribe size, and the effect of p on bribe size, depend on whether punishment is symmetric or not. Under perfect symmetry, bribe size stays constant at<sup><u>L</u></sup> 2<sup>aslongaspunishment</sup> 7
<!-- Start of picture text --> Be<br>(8 > 0)<br>! (Fo> Fe; B = 0)<br>E j (Fo= Fe: B = 0)<br>;<br>0 L 1 P<br>(Fo + Fe)<br><!-- End of picture text -->
whistle-blowing must be incorporated in the entrepreneur’s utility, so that:<sup>7</sup> We use a modified rational expectations approach to define equilibrium: First, B<sup>∗</sup> (p) is determined taking p as given (if there is no solution, a bribe is not requested). Subsequently, the entrepreneur chooses p according to some function p<sup>∗</sup> (B). In equilibrium, the p assumed during bribe size negotiations must be the same as the actual p the entrepreneur selects.<sup>8</sup> For (p<sup>∗</sup> , B<sup>∗</sup> ) to constitute an equilibrium, it must satisfy p<sup>∗</sup> = p<sup>∗</sup> (B<sup>∗</sup> ) and B<sup>∗</sup> = B<sup>∗</sup> (p<sup>∗</sup> ).

Second, suppose the state controls p. On the one hand, bribe size is determined by Nash bargaining. Given p, the optimal bribe size depends on the function B<sup>∗</sup> (p), from equation (5). On the other hand, depending on the state’s incentives, p possibly depends on bribe size, resulting in a function p<sup>∗</sup> (B).<sup>9</sup> An equilibrium with bribery, if it exists, is denoted by the pair (p<sup>∗</sup> , B<sup>∗</sup> ) that satisfies p<sup>∗</sup> = p<sup>∗</sup> (B<sup>∗</sup> ) and B<sup>∗</sup> = B<sup>∗</sup> (p<sup>∗</sup> ). The bribe size must be a best response to the detection probability, and vice versa.

# 4.1 Entrepreneur Chooses p

Suppose now the benchmark detection probability, set by the state, is <u>p</u> < 1, ̄ but the entrepreneur can raise the probability to some p ∈ <u>(p, 1]</u> at a cost k.<sup>10</sup> So, To make the problem interesting, we assume that <u>p</u> is low enough to support bribery: The Nash bargaining solution, if it exists, for either p ∈ �p, ̄p� is given by:

> 7 This continues to satisfy the convexity requirements of the Nash Bargaining problem.

> 8 This is a non-standard concept of equilibrium as it combines cooperative and noncooperative choices. Intuitively, a way to think of this within the standard framework of a non-cooperative game is the following: consider simultaneous moves made by two “players,” where one player is the entrepreneur who must choose p and the other player is the entrepreneur-offi cial pair who must choose B according to their own objective function which, in this case, is provided by Nash bargaining.

> 9 It is not being assumed that the government knows in advance what the bribe size will be, but that it has a rational expectation about the size of bribe for this class of crime. Note that this includes the special case where p<sup>∗</sup> (B) remains unchanged across different values of B.

> 10 For ease of exposition, we assume there are only two possible values of p. It is straightforward to extend the analysis to a continuum of possible values. Notes are available upon request.

9
<!-- Start of picture text --> B<br>p*(B)<br>t} og |<br>on<br>s<br>L~k sy BY) |<br>> \ an<br>Na<br>0 BR Pp L 1 °<br>(Fo+ Fe)<br><!-- End of picture text -->
recovery is suffi ciently large, so:<sup>12</sup> We can now analyze the impact of a switch from perfectly symmetric to perfectly asymmetric punishment in two cases. First, suppose the highest detection probability still allows a bribe to be given (p ̄ < FLO<sup>).Anequilibrium</sup> with a bribe size of B<sup>∗�</sup> <u>p�</u> and detection probability <u>p</u> exists if each is a best response to the other; that is, using (10) and (11), if An equilibrium with bribe size of B<sup>∗</sup> ( ̄p) and detection probability p ̄ exists if each is a best response to the other; that is, using (10) and (11), if It can easily be verified that kH > kL, so there is a range of parameter values that supports two equilibria—one with low detection and small bribes, and another with high detection and large bribes.

Next, suppose a bribe is impossible at p ̄ (p ̄ ≥ FLO<sup>).Anequilibriumwithlow</sup> detection exists if k > kL as defined above. Otherwise, if k ≤ kL, an equilibrium with bribery cannot survive. This is summarized in the next proposition.

Proposition 2 Consider a switch from symmetric to asymmetric punishment. (1) If p ̄ < FLO<sup>,briberywillnotbeeliminated.Fork>kL,therewillbe</sup> ak ≤uniquekH , thereequilibriumwill be witha uniqueB<sup>∗�</sup> <u>pequilibrium�</u> and <u>p,</u> aswithunderB<sup>∗</sup> symmetric( ̄p) and p ̄. Forpunishment.k ∈ (kL, kForH ], there will be two equilibria.

(2) If p ̄ ≥ FLO<sup>andk>kL,therewillbeauniqueequilibriumwithB∗�</sup> <u>p�</u> and <u>p,</u> as under symmetric punishment. If p ̄ ≥ FLO<sup>andk≤kH,thelicenseis</sup> delivered without a bribe.

We now discuss the proposition intuitively. For bribery to exist, there must be an equilibrium bribe size (B<sup>∗</sup> ) and detection probability (p<sup>∗</sup> ) such that p<sup>∗</sup> is a best response to the bribe size and B<sup>∗</sup> is a “best response”to the detection

> 12 We are assuming that, when indifferent, the entrepreneur chooses the higher detection probability.

11
probability. In other words, p<sup>∗</sup> should be such that the entrepreneur’s benefits from whistle-blowing are greater than the costs of doing so. p<sup>∗</sup> (B) is (step-wise) rising in B—under perfectly asymmetric punishment, a higher bribe means he stands to gain more from whistle-blowing. And B<sup>∗</sup> should be such that, given p, the bribe maximizes the Nash product or, in this case, divides the surplus equally across both parties. The possible equilibrium outcomes are depicted in Figures 3-6. A bribery equilibrium exists if the best response functions intersect.

If k is low, whistle-blowing is cheap. So, for a given bribe size, the entrepreneur is more willing to set a high p. The best response to a high p is a high bribe size. But if p ̄ is high enough, it is impossible to find a bribe size for which the probability of detection will be low enough to generate any surplus. So there will be no intersection of the best response functions (Figure 3). The offi cial will provide the license without asking for a bribe.

The above analysis shows that, even in this more realistic framework, the basic logic of asymmetric punishment (Basu, 2011) remains intact in that it encourages whistle-blowing, but at the same time the model demonstrates that the control of corruption has greater complexity than suggested in that paper. If asymmetric punishment encourages enough whistle-blowing, bribery is eliminated. But, if whistle-blowing is expensive or there are limits to how high detection probability could go, bribes might get bigger under asymmetric punishment. If k remains low enough to encourage whistle-blowing and p ̄ is low enough to sustain bribery, asymmetric punishment simply leads to a rise in the bribe size which must occur to account for the higher likelihood of detection (Figure 4).

Finally, if k is high enough, the low bribe outcome continues to survive in equilibrium. At such a bribe size, the entrepreneur does not have the necessary incentives to raise p. If k is very high, this is the only equilibrium (Figure 5). For intermediate values of k, two equilibria can coexist (Figure 6). However, in such cases, since the high detection equilibrium is Pareto dominated, we might conjecture that it is unlikely to be selected.<sup>13</sup>

# 4.2 Costly Adjustment of p by the State

There are two reasons the state might prefer to encourage revelation by citizens rather than relying on its own detection. The first is that detection by the state could be particularly costly. To detect bribery, it has to be vigilant across all transactions, even those where no bribes are exchanged. On the other hand, it

> 13 Though Dufwenberg and Spagnolo (2013) emphasize a different and complementary set of considerations, it is useful to contrast our results to those in their benchmark game. In their model, if the offi cial incurs a cost of delivering the license, asymmetric punishment induces the offi cial to reject any offered bribe but to also not deliver the license (a bribe functions as compensation for the offi cial’s costs, and asymmetric punishment makes it impossible for the offi cial to be compensated). In the current paper, even if we were to introduce costs associated with license delivery, our results would remain qualitatively unchanged (asymmetric punishment could eliminate bribery or cause a rise in bribe size). This is because we implicitly treat not delivering the license as a dereliction of duty that subjects the offi cial to punishment as if he had demanded a bribe.

12
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might be cheaper for individuals to reveal that bribery has occurred, since they know exactly who was involved and how much was exchanged.

The second is that a government that would like to detect bribery would still have to rely on an enforcer who is himself subject to a cost-benefit analysis. As we argue next, while one can easily see how it would be in the interest of a decriminalized bribe-giver to have the bribe detected, this is less clear in the case of a government enforcer. Suppose p is set by a government enforcer at cost c (p). We could ask how the incentives for the enforcer should be set up.

First, note that it is very hard to incentivize the enforcer to minimize the incidence of bribery. Since the state cannot distinguish between p = 0 (under which no bribes will be detected) and p = 1 (under which bribery will actually be eliminated), the enforcer has no incentive to exert any effort to raise p. Bribe-enforcers have less of an incentive to eliminate bribery than bribe-givers do. Alternatively, suppose the bribe-enforcer is rewarded by the number of bribes detected or the amount in bribed detection. This actually incentives higher detection probabilities, but it is never in the enforcer’s interest to raise detection so high that bribery is eliminated.

# 5 Discussion and Conclusion

In the preceding sections, we built a simple model of harassment bribes. If a government offi cial demands a bribe in exchange for his service, he and the entrepreneur must bargain over the bribe size. The offi cial demands a bribe only if a Nash bargaining solution exists (given our construction of threat points, existence of a solution ensures that the offi cial is better off by demanding a bribe than otherwise). Bribe size rises in detection probability, the offi cial’s fine, and fraction of bribe the offi cial must repay if detected. Bribe size drops in the entrepreneur’s fine. Importantly, these bribe size effects exist solely to reallocate surplus. They should not be viewed as indicators of the severity of corruption. We find that the incidence of bribery does not depend on the symmetry properties of punishment. A bribe is paid as long as the total expected fines are less than the surplus generated by the license. To eliminate bribery, the state must raise expected punishment to a suffi ciently high level. If punishment is raised but inadequately, bribery will persist with higher bribe sizes.

To examine more carefully the implications of asymmetric punishment, we expanded the model to endogenize detection probability. If the offi cial demands a bribe, the entrepreneur must choose detection probability. Now, the symmetry properties of punishment matter. Under symmetric punishment, endogenous selection of detection probability changes nothing since it is not in the entrepreneur’s interest to have the bribe detected. However, under asymmetric punishment, the entrepreneur is willing to incur some costs to raise detection probability as this allows him to get his money back. If bribery survives, bribe size and detection probability must be best responses to each other. We find that asymmetric punishment eliminates bribery if whistle-blowing is effective and cheap. Otherwise, bribery survives and bribe sizes can rise relative to sym15
# metric punishment.

Our results here are quite parameter-specific, and importantly so. Consider variation in k and p ̄. These two variables describe the ease with which a citizen can reveal bribery to the government, and they depend on the ability to verify a bribe payment, the responsiveness of government departments to such claims, the extent to which the whistle-blower is protected after the act, the effectiveness of the judicial system, etc. If k is low and p ̄ high, so the country has the infrastructure to allow reporting at low cost, asymmetric punishment is an effective solution for eliminating bribery. The change in the entrepreneur’s incentives drives detection probabilities so high that it is impossible to arrive at a bribe size that is large enough to make bribery worthwhile for the offi cial. As k rises and p ̄ drops (i.e. whistle-blowing gets more diffi cult), we move from zero bribery to large bribe sizes. As k rises further, bribe sizes drop down to the levels under symmetric punishment. This leads to some unusual cross-country predictions. If countries were ordered by ease of reporting bribes, all else equal, we should see bribery appear the most severe for intermediate countries where whistle-blowing is cheap enough that a lot of it happens, but not so cheap that bribery can be eliminated. The possibility of multiple equilibria adds additional complexity, as identical underlying conditions could lead to substantially bribe sizes.

This model suggests some ways to structure our thinking about anti corruption policy. Clearly, one way to eliminate bribery is to make punishments severe and probability of detection high (see Becker, 1968). However, severe fines are often politically infeasible and detection, if carried out by government enforcers, can be expensive (where should we look?) and hard to incentivize (how do we distinguish between eliminating bribery and failing to detect it?). In this context, it makes sense to transfer the task to signaling bribery to those who know it best—the parties involved. This can be incentivized through asymmetric punishment. But for asymmetric punishment to work, whistle-blowing needs to be suffi ciently cheap—the state must not only encourage entrepreneurs to reveal bribery, it must allow them to do so easily. This requires careful attention to several aspects of bureaucratic and legal institutions. If the state is unable to make whistle-blowing suffi ciently cheap to eliminate bribery, then somewhat perversely, it is best to make whistle-blowing expensive so it happens less. This is because the effort expended in revealing a bribe creates a pure surplus loss unless bribery is actually eliminated. So, if countries with bribery problems are also countries with weak institutions for reporting, they can be stuck in corruption traps where asymmetric punishment makes matters worse, not better.

The model above is stylized to isolate some key effects. There are some natural extensions that could help build a richer understanding of the design and implications of anti-corruption policy. First, the model could be extended to non-harassment bribes. Consider the following example: the agent has violated the law and stands to lose L. Instead, he could pay a fine B to the bureaucrat. The problem remains identical to ours but notions of effi ciency might change. This also creates room for thinking about endogenizing the agent’s decision to 16
commit the crime in the first place.

Second, it might be instructive to analyze a setting with heterogeneity in license benefit and moral costs, where these are private information.

Finally, recall that one prediction of our model is that if fines are small, bribe sizes can get indefinitely large as the probability of detection approaches one. While it could be argued that lim<sup>isnotempiricallyrelevant,this</sup> p→1<sup>B∗(p)</sup> does raise a concern about the depths of entrepreneurs’ pockets. Our model could quite easily be re-analyzed with an additional “liquidity constraint.”This will serve to discourage bribery. Also, tight liquidity constraints could raise the effectiveness of asymmetric punishment by making it more likely that the intersection of the best response functions lies outside the acceptable range of bribe sizes. When populations are poor, this constraint can be expected to be tight. As countries grow and pockets get deeper, the liquidity constraint will loosen and corruption will rise. Simultaneously with growth, we might expect an improvement in institutions and the costs of whistle-blowing, which could deter corruption. How these countervailing effects affect outcomes is a potentially interesting question for continuing empirical and theoretical analysis.

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