Nonverifiability in agency theory

When two parties engage in a relationship, it is often the case that they are uncer- tain about the value of some parameter that will affect their future gains from trade. This uncertainty is represented by assuming that the parameter can take several values, each value corresponding to different states of nature whose prob- ability distribution is common knowledge. In this chapter the parameter will take two values. Even though they will both learn the value of the parameter in the future, the trading partners cannot write ex ante contracts contingent on the state of nature, because this state of nature is not verifiable by a third party, a benev- olent court of law, that could enforce their contract. As the following quote from Williamson (1975) suggests, such situations might entail transaction costs:

Both buyer and seller have identical information and assume, further- more, that this information is entirely sufficient for the transaction to be completed. Such exchanges might nevertheless experience difficulty if, despite identical information, one agent makes representations that the true state of the world is different than both parties know it to be and if in addition it is costly for an outside arbiter to determine what the true state of the world is (p. 32).

The goal of this chapter is to assess whether the nonverifiability of the state of nature significantly affects the ability of the contractual partners to realize the full gains from trade. More precisely, we ask whether this nonverifiability has any bite in the realm of complete contract theory, i.e., when the principal has the full ability to commit to a mechanism at the ex ante stage and a benevolent court of law is available, as we assume throughout this whole volume. Actually, we show that the nonverifiability of the state of nature alone does not create transaction costs under those assumptions.

Section 6.1 starts with a useful benchmark and considers the case where the principal and the agent do not write any contract ex ante. Bargaining over the gains from trade takes place ex post, i.e., once the state of nature is commonly known. If the principal has all the bargaining power ex post, the first-best allocation is implemented, with the agent being maintained at his status quo utility level.1 If we had considered a more even distribution of the bargaining power ex post, allocative efficiency would still be preserved, but the distribution of the gains from trade would be more egalitarian: the principal (resp. the agent) would obtain a lower (resp. higher) utility level. Hence, if the principal does not expect to have all the bargaining power at the ex post stage, he strictly prefers to design a mechanism at the ex ante stage when he still has all the bargaining power. Similarly, ex ante contracting may also be preferred when the principal is risk averse and thus has an ex ante demand for insurance. In section 6.2, we argue that the simple incentive contracts already analyzed in an adverse selection context with ex ante contracting in chapter 2 perform quite well in the case of nonverifiability and risk neutrality of the agent. Efficiency is always achieved when the Spence- Mirrlees property is satisfied for the agent’s objective function. However, in the case of nonresponsiveness, or when the agent is risk averse, the optimal ex ante contract entails inefficiencies.

To circumvent this weakness of ex ante contracting, in section 6.3 we elab- orate a more complex mechanism that always achieves the first-best with Nash implementation.2 The principal offers a mechanism that is designed to ensure that the noncooperative play of the game by both the principal and the agent yields the desired first-best allocation. In this context, we extend our methodology of chapter 2 and prove a revelation principle when both the principal and the agent simultaneously report messages over the state of the world to a benevolent court of law. In playing such a two-agent mechanism, the principal and the agent adopt a Nash behavior. An allocation rule is implementable in Nash equilibrium if there exists a mechanism and a Nash equilibrium of this mechanism where the agents follow strategies that induce the desired allocation in each state of the world. Then, we show that the standard principal-agent models are such that the first-best is implementable in Nash equilibrium with rather simple mechanisms.

However, Nash implementation may not be sufficient to always ensure that a unique equilibrium yielding the desired allocation exists in each state of nature. Multiple equilibria may arise, with some being nontruthful. In other words, an allocation rule may fail to be uniquely implementable. We then define the notion of monotonicity of an allocation rule and show that unique Nash implementation implies monotonicity. For allocation rules that fail to be monotonic and thus do not allow unique Nash implementation, the important question is whether one can build more complex mechanisms, possibly with sequential instead of simulta- neous moves, that still allow unique implementation. In other words, is it possible to design an extensive form game whose subgame-perfect equilibrium uniquely implements a given allocation rule? In section 6.4 instead of providing a full the- ory of subgame-perfect implementation, we construct a simple extensive form that solves the problem in a specific example. Finally, section 6.5 presents some exten- sions for the case of risk aversion, and section 6.6 offers some concluding remarks about the nonverifiability paradigm.

Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.

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