6 Self-enforcing corruption

Information transmission and organizational response

Lambros Pechlivanos

Introduction

Organizations usually consist of individuals who share neither the same goals nor the same information. In such an environment, motivational issues are far from trivial problems to resolve. The principal–agent model is the simplest framework used to analyse such situations (e.g. Holmström 1979; Grossman and Hart 1983). As the number of members in an organization increases, however, the design of the optimal grand contract becomes more complicated. A number of them may collude, thus creating a new set of restrictions to be dealt with. A plethora of different results about optimal contract designs have been reached, depending on whether these side-contracts lead to actions that may be beneficial or detrimental to the organization, or whether information transmission is facili- tated or not (Holmström and Milgrom 1990; Itoh 1993; Tirole 1986).¹

Collusion does not occur only between members of an organization. Some members may also collude with outside parties, possibly at the expense of the organization as a whole. However, the principal does not necessarily have power over non-members. Her²ability to discipline outside parties may be restricted.

In this case the principal can design policies that affect only her agents. A full- blown mechanism design approach might not be appropriate, and therefore a more circumstantial analysis of potential policy instruments is needed. As a con- sequence, collusion usually occurs in equilibrium. This is the situation this chapter concentrates on.

A common feature of the literature is the assumption that all parties have the ability to write enforceable contracts.³This assumption is not innocuous when analysing side-contracts. Departing from this approach, this chapter attempts to explain explicitly the procedures under which such side-contracts may be enforced. The mechanism that is used to enforce the desirable behaviour is per- suasion through manipulation of future returns. If the parties involved interact repeatedly, an implicit threat of retaliatory behaviour in the future may be suffi- cient to deter any deviation from collusion.

Examples of collusion among members of an organization and outside parties are numerous. Interest groups lobbying members of legislative bodies, criminals offering kickbacks to policemen or citizens bribing low-rank

administrators to bypass red tape are just a few common examples of corrupt activities. Although these phenomena are far more pervasive in the public sector, private institutions are not immune.

The framework employed to analyse such phenomena is a principal–agent–

client model. Consider the following situation. A clientele needs the services of an organization to accomplish a task. The organization is structured as a two- tier hierarchy, in which a principal oversees a group of agents. Each client is ran- domly assigned to an agent with whom she has to deal indefinitely and who is the only one that can provide this service to her. Assume that there is an incen- tive for the client to persuade the agent to bypass regulations and that she is willing to reward him for the favour. To help the client, the agent must under- take a costly action which is not observable by the client. Such side-contracts are assumed to be prohibited by the contract governing the principal–agent rela- tionship. This implies that corrupt side-contracts are not enforceable by an external authority and therefore, for illicit trade to take place, the client must rely on the agent’s goodwill to return the favour.

Before any transaction takes place, the principal designs the policy instru- ments she will have at her discretion to control her agents and to deter corrup- tion.⁴ Being conscious of the self-enforcing nature of the client–agent relationship, the principal would like to manipulate the information the client collects about the agent’s behaviour. It is in the interest of the principal to implement policies that garble the information that reaches the client. As has been shown in the literature of repeated games (Kandori 1992a), the worse the informativeness⁵of the signals observed by the players, the lower the degree of cooperation that can be sustained. The reasoning goes as follows. Collusion is sustainable only if the client and the agent can punish non-conforming behav- iour. Threats of punishments, though, are effective only if the players can infer that such behaviour has occurred. Obviously, the effectiveness of such arrange- ments depends on the precision of the inferences made, which in turn depends on the information the two players receive about each other’s actions.⁶

The premise of this chapter is that the reliance of self-enforcing relationships on informational flows is important when evaluating the effectiveness of the principal’s policies. The goal is to characterize the principal’s optimal policies when facing self-enforcing client–agent relationships – in contradistinction to the optimal policies had the same relationships been enforceable. Hence, the analysis concentrates on instruments that affect the informational flows between the client and the agent. These instruments include (a) the auditing of the agents’ performance, and (b) the imposition of penalties on the agents.⁷

It should be stressed that the term ‘auditing’ does not refer to an ex post evaluation of the agent’s behaviour, but rather to a proactive monitoring of the agent’s decisions. The principal, acting as a monitor, has the authority to review her agents’ decisions. She can either rubber-stamp what her agents have decided (i.e. choose not to audit), or thoroughly review and then accept it or reverse it.

Within this framework, auditing serves a double role. First, it is useful because it allows the principal to intercept corrupt activities and negate them. Hence, 94 Lambros Pechlivanos

clients may have less of an incentive to bribe for services they may never receive.

But, additionally, and more interestingly for the purpose of this chapter, even if auditing is not observed by the client it is also useful because it garbles the information the client receives about the agent’s behaviour.

The following example illustrates this point. Consider a real estate developer (the client) whose business is concentrated in a certain region and who must acquire a permit from the zoning authorities in order to build on each property she wants to develop. Of course, it is in the client’s interest to build in excess of the established regulations, and she is willing to bribe a bureaucrat in the zoning office to bring this about. The bureaucrat (the agent) has the discretion to give the permit or to stop the project, depending on its compliance with reg- ulations. If he decides to help the developer and accept the project, he has to undertake costly actions to support his decision (find loopholes, fabricate docu- ments, etc.). His decisions, however, are subject to review from his superior (the principal). In the end, the developer either receives the permit or is asked to make changes to comply with the regulations. When receiving a negative response, the developer is not able to infer with certainty whether the bureau- crat attempted to help but was audited, or did not bother to support the pro- posal even though he was bribed.

The imposition of penalties has two countervailing effects. Obviously, an agent is less willing to consent to his client’s wishes if he knows that he would be punished when caught. On the other hand, if penalties are observable by the client, their imposition increases the client’s information about the agent’s performance and facilitates collusion.⁸ There exists a trade off between the deterrent power of the punitive measures inflicted upon the agent and the addi- tional information they provide the client with respect to the agent’s past behaviour. It looks plausible that there is a positive correlation between the severity of penalties and their observability by outsiders. In most judicial systems, the more ambitious the prosecution’s goal the more concrete must be the proof of guilt, and thus the more visible the whole process becomes. Hence, the principal might prefer to impose mild penalties at the expense of deterring fewer agents in order to decrease the observability of the penalties, thus retain- ing the enforceability problems in the remaining corrupt relationships.⁹

Since punishment entails no direct cost to the organization, it seems plaus- ible that the principal should set the penalties high enough to deter such agents completely. In that case, there would be no ongoing collusion to worry about.

However, in practice we rarely observe prompt and severe punishment in cases of detected corruption (Klitgaard 1988). In most administrations, the proce- dures are convoluted and usually end up being resolved in courts. Moreover, several theoretical justifications have been put forth for the non-optimality of infinite penalties, ranging from the inducement of marginal deterrence to the presence of imperfections in detection technology (an innocent could be found guilty) coupled with risk-averse agents.

In addition, we find that penalties have another effect: they differentiate between deterred and undeterred agents, thus creating a new source of

uncertainty for the client. Moreover, this type of uncertainty, which depends on agent characteristics, may facilitate collusion. The undeterred agents want to build a ‘reputation’ for being corrupt, and this extra incentive increases their eagerness to abide by their side-arrangements.

In this chapter, the second section (pp. 96–100) models and characterizes the repeated client–agent relationship under auditing. The third section (pp. 100–1) describes the optimal intensity of auditing. The fourth section (pp. 102–6) introduces heterogeneity among agents and describes the effects of penalties on the relationship. The fifth section (pp. 106–7) discusses the optimal severity of penalties. Finally, conclusions are presented (pp. 107–8).

Client–agent relationship

Before clients and agents start interacting, the principal announces her policies and commits to following them. Specifically, she sets the probability that she will audit her agents and the penalty she will inflict upon corrupt ones. Subsequently, each client is randomly assigned to an agent, with whom she will interact there- after. In the current section, the focus is on the effects of auditing. The character- ization of the effects of the imposition of penalties is deferred until the fourth section (pp. 102–6). This allows us to separate the effects of the two policies.

Stage game

There are two active players, the client and the agent, each of whom takes an action. Since the principal acts before the client–agent relationship begins, her actions are taken as given by both the client and the agent. This allows us to represent auditing as a random variable. Given the realization of the auditing event, payoffs are distributed. The official aspects of client–agent interaction are not modelled explicitly; neither are the payoffs accrued to all players because of them. For simplicity, the net benefits resulting from the official activity are nor- malized to zero. Hence, all benefits or costs of corruption described below are above and beyond the official ones.

The exact timing of the game is as follows. First, both players simultaneously choose their actions. The client decides whether to pay a ‘bribe’ to the agent (a^C∈{b, nb}), and the agent decides whether to deliver the ‘favour’ to the client (␣^A∈{d, nd}). Afterwards, the agent observes whether auditing occurred (sA) or not (sN) (␻∈{sN, sA}), with p⫽Prob(␻⫽sN). Finally, as a result of the agent’s action and of the realization of the random variable, the client observes whether she received the favour (y∈{f, nf}), and, as a result of the client’s action alone, the agent observes whether he was bribed. The metaphor of reciprocal trade to represent this situation will often be used. Consider that a bribe is traded for a favour:

•____________________ •___________________•____________________•

client chooses a^C; ␻is observed by client observes y;

agent chooses ␣^A the agent agent observes a^C 96 Lambros Pechlivanos

It is assumed that the client’s decision to bribe and the agent’s decision to deliver the favour are costly to them (where the cost is denoted by K). Never- theless, the benefit enjoyed by the recipient (denoted by B) is larger, thus allow- ing for mutual gains from trade.¹⁰If auditing occurs, the client does not receive her favour, although the agent may have taken the necessary action and has already incurred the cost. The payoffs to the players are represented by the normal form presented in Figure 6.1. This figure helps us understand the nature of the imperfect monitoring of the agent’s action by the client. When the client finds that she did not receive the favour, she cannot be certain whether the agent defected or was cooperating but audited.¹¹In contrast, the agent has full information throughout the game.

It can be seen clearly that the stage game has a unique equilibrium under which the agent cannot be trusted by the client, and therefore the equilibrium strategies are, for the client, not to bribe and, for the agent, not to deliver the favour. Hence, the maxima value sustained in equilibrium is v⫽(0,0).

Figure 6.1 Stage-game normal form representation.

If no auditing

If auditing

Agent Deliver Not deliver Client

Bribe Not bribe

Agent Deliver Not deliver Client

Bribe Not bribe

B–K, B–K ⫺K, B B, ⫺K 0, 0

⫺K, B–K ⫺K, B 0, 0 0, K

Repeated game

In the infinitely repeated game, after every period, both players accumulate their observations and form a history of the way the game is played. As was argued in the previous section, the agent observes all actions and realizations of outcomes, and therefore he has information about the whole history of the game.¹²In con- trast, having observed only her own actions and reception of favours, the client’s information is partial. Formally, strategy profiles (sC, sA) are pairs of infi- nite sequences of mappings from histories to actions. In each period, a pure action profile ␣⫽(␣C, ␣A) induces a probability distribution over the reception of favours ␲(y|␣^A, ␻). The observational reception of favours is compounded with past observations to form the history of the game. The players’ actual per period payoffs are denoted by the pair r⫽(rC, rA). Hence, expected per period payoffs can be computed as g(␣)⫽∑y∑␻r(␣, ␻) ␲(y|a^A, ␻). If needed, mixed strategy profiles (␴C, ␴A) can be equivalently defined. When mixed action pro- files ␣(␣) are considered, the induced probability distribution over outcomes can be easily computed as ␲(y|␣^A, ␻)⫽␲(y|␣^A, ␻) ␣^A(␣^A) and expected per period payoffs can be defined as g(␣)⫽∑y∑␻∑␣(␣)r(␣, ␻)␲(y|a^A, ␻). Finally, it is assumed that both players discount payoffs between periods at a rate of ␦E(0, 1).

The objective of the players is to maximize their normalized present value:

max vi⫽(1⫺␦) Eaⁱt

冦 ^冱

^t⫽^⬁1

␦^t⫺1gi(at)

冧

^{, i⫽A, C}

{^ait}t^⬁⫽1

The goal of the exercise is to find the maximum payoff that can be supported by a perfect public equilibrium, given the environment created by the principal, parameterized by p, and the discount rate.

Repeated game equilibria analysis

To solve for the equilibrium of the repeated game, in principle, one should con- sider all possible strategies, which may be highly non-stationary. Nonetheless, as the game is characterized by imperfect public information, the self-generation and factorization properties of Abreu, Pearce and Stacchetti (1986, 1990) can be employed, and it can be shown that all attainable equilibrium payoffs can be derived using strategies that follow a first order Markov process. Moreover, because the game has the special feature of having only one-sided imperfect monitoring, attention can be further restricted, without loss of generality, on public strategies.¹³ Hence, the strategy space can be parameterized by the following eight probabilities:¹⁴

For the client: ␤f, b⫽Prob(b|f,b) ␤f,nb⫽Prob(b|f,nb)

␤nf, b⫽Prob(b|nf,b) ␤nf,nb⫽Prob(b|nf,nb) For the agent: ␥f, b⫽Prob(d|f,b) ␥f,nb⫽Prob(d|f,nb)

␥nf, b⫽Prob(d|nf,b) ␥nf,nb⫽Prob(d|nf,nb) 98 Lambros Pechlivanos

Obviously, the stage game equilibria continue to survive in the repeated game.

Hence, the myopic repetition of the unique stage game equilibrium constitutes an equilibrium of the repeated game. This equilibrium, however, does not exploit the gains possible from cooperation. The goal is to characterize the most collusive equilibrium, given the environment within which the players interact.

According to the bang-bang rewards property, it is possible to span the entire equilibrium payoff set by considering only extreme values for the con- tinuation payoffs (Abreu, Pearce and Stacchetti 1990). Behind this property, though, is the implicit assumption that the ‘public signal space’ is continuous.

When the signal space is continuous, one can keep the values of the ‘reward’

and ‘punishment’ continuations at their extreme values (i.e. use only extreme continuation payoffs) and trace the whole equilibrium payoff set by altering the partition of the signal space. Hence, the largest value of the equilibrium payoff set can be attained by fine-tuning the partition of the public signal space. In essence, the goal is to concentrate the ‘punishment phase’ in the region that is as informationally efficient as possible (Pearce 1992). In this model the public signal space is discrete (it is the bribing decision cum the reception of favour), and hence the preceding argument does not, literally, apply. Generically, it is impossible to attain the largest equilibrium payoff in this way because the ‘pun- ishment phase’ cannot be concentrated in the most informationally efficient region. Therefore, what one should do to increase the value of the attainable equilibrium payoff is to make the ‘punishment’ continuation payoff as large as possible, so long as it does not destroy the players’ incentives to behave cooper- atively.

The following proposition characterizes the equilibrium strategies that sustain the most collusive equilibrium outcome. This proposition, as well as the subsequent ones in the chapter, will not be proved here; interested readers are referred to Pechlivanos (1997).

Proposition 1

There exist two cut-off values p*⫽K/␦B and ␦⫽K/B, such that for all pⱖp*

and ␦ⱖ␦, the following strategies construct a mixed strategy equilibrium which is more collusive than any of the pure strategy equilibria of the game:

␤^mf, b⫽␤^mf, nb⫽1 ␥^mf, b⫽␥^mnf, b⫽1

␤^mf, nb⫽␤^mnf, nb⫽ᎏ␦p

␦ B p

⫺ B

ᎏK ␥^mnf, b⫽␥^mnf, nb⫽ᎏ␦p

␦ B

p

⫺ B ᎏK

Essentially this equilibrium prescribes that the players take cooperative action as long as the public signal they observed in the preceding period is beneficial to them.¹⁵On the other hand, if the two players did not observe a beneficial public signal, they take an action that hinders cooperation (as they may take the non- cooperative action with positive probability). The probability with which they

take the non-cooperative action is computed such that the players are simply indifferent with regard to being interested in continuing their cooperation in the future or not.¹⁶

Conducting comparative statics on the equilibrium strategies, we find that at the most collusive equilibrium all probabilities are weakly increasing in p. This means that, as auditing becomes less frequent, the right incentives can be given to the players even with less-intensive schemes. This is possible because as p increases, reception of favour is a more accurate signal of delivery, and hence the client can punish the agent in an informationally more efficient region. This reduces the probability of entering into a ‘punishment phase’ along the equilib- rium path. Since the incentives are provided in terms of expected payoff differ- entials, when punishment becomes less ubiquitous, the same incentives can be provided with less intensive punishment.

The same comparative statics results carry on with respect to equilibrium payoffs. Given equilibrium strategies, the largest normalized equilibrium payoff for each of the two players is readily calculated: v^mC⫽pB⫺Kandv^mA⫽B⫺1/pK.

Summing up the two payoffs, one can find that the largest value of corruption that can be sustained using a self-enforcing arrangement is

v^m⫽(1⫹p)B⫺ᎏ1⫹ p

ᎏpK.

Clearly, v^mis increasing in p. Moreover, it is less than the first best payoff for all p. This result can be summarized with the following proposition:¹⁷

Proposition 2

The maximum perfect public equilibrium payoffs that can be supported by mixed strategies are strictly decreasing in the probability of auditing.

Optimal auditing

Auditing is costly to the principal. It requires that she spend resources and time to monitor transactions.¹⁸To ensure that the principal is not able to shut down the whole activity, it is assumed that the cost of auditing all activities is prohibi- tive. More rigorously, let the cost of auditing be denoted as C. An interior solu- tion is ensured by the following Inada-like conditions:

C⬘(p)⬍0, C⬙(p)⬎0, C⬘(1)⫽0, C⬘(p*)⫽⫺⬁and C(p*)⬎2(B⫺K).

Before discussing the principal’s optimal auditing decision, one should analyse, as a benchmark, the case in which client and agent can write enforceable con- tracts. In this case, the two players are able to consummate all potential gains from trade. To see this, consider the following side-contract, enforceable by a third party, between the client and the agent:

100 Lambros Pechlivanos