Corruption driven by imitative behavior

doi:10.1016/j.econlet.2012.04.092

Economics Letters

Volume 117, Issue 1, October 2012, Pages 84-87

https://doi.org/10.1016/j.econlet.2012.04.092 Get rights and content

Abstract

One can restructure institutions, but if individual-level motivations for corrupt behavior are not understood, these restructuring may not be effective. We introduce an evolutionary-game modeling to deal with the problem of corruption driven by imitative behavior.

Highlights

► We develop an evolutionary dynamics to study corrupt behavior. ► There exists a threshold from which agents prefer to follow a non-corrupt behavior. ► A key variable is the reviewing rate of imitation for the choices of behavior.

Introduction

Corruption is defined as behavior that deviates from implicit or explicit behavioral norms with or without legal and ethical connotations ruled out by institutions (see Mishra, 2006). Acemoglu and Robinson (2005) pointed out that of primary importance for economic performance is the type of institutions in society, since they influence the structure of economic incentives and economic agents’ behavior.

The scourge of corruption in Mexico is a nice real example of corrupt behavior driven by imitation, i.e. to be corrupt if others are also corrupt. The tenacity of corruption in Mexico has not kept politicians from promising to eradicate it, since Mexicans correctly identify corruption either as the root of Mexico’s development problems or as the cause of a poverty trap through the cultural behavior of doing as others do (see Wydick, 2008). Corruption occurs at all levels of Mexican society, for instance, the legendary case of the 114 million dollars deposited into Swiss bank accounts by Raul Salinas, brother of the former President Carlos Salinas de Gortari, who shortly thereafter fled to exile in Ireland. The money was believed to have came through relationships with Mexican and Colombian drug cartels during his presidential period of administration of the Mexican government. Another case of corruption in Mexico was that in 2004 by Carlos Ahumada, a 40-year-old millionaire, who offered million-peso bribes to officials of Mexico’s left-of-center Partido de la Revolución Democrática to obtain lucrative sewer-cleaning contracts in Mexico city.¹ Corruption appears at all levels in Mexico as a kind of “cultural behavior”, since the word for bribe, mordida, literally means bite, and getting bitten in Mexico is regrettably common. In Mexico, mordida permeates every level of society and institutions in which individuals act because it is a norm, and they just do what others are doing (whether corrupt or not). Bribes in Mexico are common and indeed are often deemed necessary for obtaining business licenses and other types of permit. There is a popular Mexican saying: el que no transa no avanza, i.e., who does not corrupt does not move on. Of course corruption is not a norm of behavior in every country (e.g. New Zealand, Singapore, or Finland; see Transparency International on the Global Corruption Barometer, 2010),² but we wonder what accounts for adopting a corruptive behavior or not. We argue that the answer to this question is influenced by individual expectations driven by imitative behavior about the choices of others around to corrupt or not.

We present a novel model to explain why individuals imitate a corrupt behavior, thinking of it as a kind of rational behavior. Rational imitation can be explained as follows. An individual, A, can be said to imitate the behavior of another individual, B, when observation of the behavior of B affects A in such a way that A’s subsequent behavior becomes more similar to the observed behavior of B. An individual can be said to act rationally when the individual, faced with a choice between different courses of actions, chooses the course which is the best with respect to his/her interests, his/her beliefs about possible action opportunities, and the effects of these potential action opportunities (for a survey on the notion of imitation see Sanditov, 2006).

In our model, imitation results in individuals performing a spectrum of tasks “as others do”, whether corrupt or not. We assume that occasionally each individual in a finite population gets an impulse to revise his/her (pure) strategy choice (either corruption or non-corruption). There are two basic elements for modeling.

1.
First, it is a specification of the time rate at which individuals in the population review their current strategy choice, i.e., whether they are currently corrupt individuals or not. This rate may depend on the current performance of the agent’s pure strategy and other aspects of the current population state.
2.
Second, it is a specification of the choice probabilities of a reviewing individual. The probability that an $i$ -strategist will switch to some pure strategy $j$ may depend on the current performance of these strategies and other aspects of the current population state, i.e., how large the share of corrupt individuals currently is, and the types of institution in the economy.

If these impulses arrive according to independent and identically distributed (i.i.d.) Poisson processes, then the probability of simultaneous impulses is zero, and the aggregate process is also a Poison process. Moreover, the intensity of the aggregate process is just the sum of the intensities of the individual processes. If the population is large, then one may approximate the aggregate process by deterministic flows given by the expected payoffs from corruptive and non-corruptive behaviors. Weibull (1995) and Björnerstedt and Weibull (1996) studied a number of such models, in which those individual may imitate other agents in their player population, and show that a number of payoff-positive selection dynamics, including the replicator dynamics, may be so derived. In particular, if an individual’s revision rate is linearly decreasing in the expected payoff to his/her strategy (or to the individual’s latest payoff realization), then the intensity of each pure strategy’s Poisson process will be proportional to its population share, and the proportionality factor will be linearly decreasing in its expected payoff. If every revising agent selects his/her future strategy by imitating a randomly drawn agent in his/her own player population, then the resulting flow approximation is the replicator dynamics.

Section snippets

The model: institutions and corrupt behavior

Institutions, according to North (1990), are the rules of the game. This broad definition bundles norms together with institutions and is also favored by Greif (2006): An institution is a system of rules, beliefs, norms and organizations that together generate a regularity of social behavior. However, in this paper we do not consider an “institution formation”, since we consider that it is given from some external (to the individual) form which include the whole structure of rules, means of

On the dynamics of corrupt behavior

Consider that the individual’s population $i \in {c, n c}$ compromises a profile distribution $x = (x_{c}, x_{n c})$ normalized to one: $x_{c} + x_{n c} = 1$ . Individuals are absolutely rational, so they change their behavior according to the expected payoffs associated with such an adopted behavior $i$ . Assume that at time $t = t_{0}$ the profile distribution is $x (t_{0}) = (x_{c} (t_{0}), x_{n c} (t_{0}))$ , and that the profile distribution of institutions is fixed at $g = (g_{c}, g_{n c})$ .

The evolution of individual’s type $i \in {c, n c}$ depends on differences in expected

Imitation by dissatisfaction

Because of dissatisfaction with current behavior, an individual reviewer must copy the behavior of the first person he/she meets on the street, so $p_{i / j} = x_{j}$ , $\forall i \neq j \in {c, n c}$ . Then, by rearranging terms, the dynamic system (10) takes the form ${\dot{x}}_{n c} = (r_{n c} - r_{c}) x_{n c}^{2} + (r_{c} - r_{n c}) x_{n c}$ ${\dot{x}}_{c} = - {\dot{x}}_{n c},$ and after some little of algebra, we get the following chain of equalities: ${\dot{x}}_{n c} = (r_{n c} - r_{c}) x_{n c}^{2} + (- r_{n c} + r_{c}) x_{n c} = (r_{n c} - r_{c}) x_{n c} (x_{n c} - 1) .$ Note that ${\dot{x}}_{n} \geq 0$ if and only if $(r_{n c} (x) - r_{c} (x)) \leq 0$ and $x_{c} (t_{0}) > 0$ , which means that the share of

Concluding remarks

We studied an individual-level approach and tackled the question of why people engage in corrupt exchange.

The above model pointed out that corruption increases because of imitation of agents. The approach is novel, and it explains the strategic foundations and evolutionary dynamics of corruption. More generally, it illustrates the importance of thinking about corruption as “the rules of the game”: when almost everyone is corrupt, honesty is the deviant behavior. What needs to be explained under

Acknowledgments

We are grateful to Bruce Wydick for helpful comments, and Eric Maskin for stimulating the research that led to this note. We thank the publisher’s staff for providing language help, writing assistance, and proofreading the article.

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