Resumen de The Principal-Agent Matching Market

David Pérez Castrillo , Kaniska Dam

• A large set of literature contributing to the theory of incentives analyzes optimal contracts in principal-agent relationships when there exist asymmetries of information. When this asymmetry concerns an action, or a decision to be made by an agent, a moral hazard problem emerges. Several works analyze optimal contracts when only one principal and one agent interact, including the seminal works by Pauly (1968), Mirlees (1976), and Harris and Raviv (1978).

  The principal-agent contracts involve the provision of incentives and typically lead to inefficiency due to the informational asymmetry.

  The main goal of this paper is to propose a useful framework to analyze the relationship between each principal-agent pair not as an isolated entity but as a part of an entire market where several principals and agents interact. In this framework, the utilities obtained by each principal and each agent are determined endogeneously in the market. This allows us to improve over the previous approach where the agents� utilities are exogeneously given and the principals assume all the bargaining power. We consider the simultaneous determination of the identity of the parties who meet (i.e., which agent is contracted by which principal) and the contracts they sign in an environment where each relationship is subject to moral hazard.

  We model the principal-agent economy as a two-sided matching game. An outcome of this economy is an endogenous matching and a set of contracts, one for each principal-agent pair under the matching. Roughly speaking, an outcome is said to be stable if there is no individual or no relevant pair objecting the existing outcome. The paper studies the set stable outcomes of this principal-agent matching market. In particular, we consider an economy with several identical principals and several agents differentiated only with respect to their initial wealth. A pair of individuals, one principal and one agent, can enter into a relationship by signing a contract. This contract specifies the contingent payments that are to be made by the agent. Also it sets the level of investment, which together with a non-verifiable effort made by the agent, determines the probability of having a high return from the project the agent operates on. The initial wealth of the agent may not cover the amount to be invested and hence, the wealth differences imply differences in liability.

  We begin by providing a complete characterization of the set of stable outcomes of the principal-agent economy. The first simple property we prove is that all the principals earn the same profit in a stable outcome. In particular, if the principals constitute the long side of the market, their profits are zero. The second feature is that the contracts offered in a stable outcome are Pareto efficient, i.e., it is not possible to increase the utility level of the principal without making the agent strictly worse-off. More interestingly, in a stable outcome, the matching itself is efficient, in the sense that it is the one that maximizes productive efficiency. For example, if the agents are in the long side of the market, only the wealthier ones, i.e., the more attractive ones (and all the principals) are matched. Third, the productive efficiency of a contract signed in a stable outcome increases with the wealth of a matched agent. That is, the richer the agent, closer is his contract to the first-best. The additional surplus generated due to this increase in efficiency accrues to the agents. Finally, the contracts signed in a stable outcome of this economy are more efficient than principal-agent contracts, i.e., the contracts signed when the principals assume all the bargaining power.

  The previous characteristics of the set of stable outcomes have very relevant policy implications when applied to particular environments. For example, consider an economy where landowners (principals) contract with tenants (agents) who are subject to limited liability. Suppose that the government would like to improve the situations of the tenants by endowing the agents with some additional money. Our analysis suggests that the government will be interested in creating wealth asymmetries among tenants since otherwise, the landowners would appropriate all the incremental surplus intended to the tenants.

  We establish a close relationship between the concept of stability and that of a competitive equilibrium. From the point of view of matching theory, one can see our model as a generalization of the assignment game with several buyers and sellers described by Shapley and Shubik (1972). We further consolidate stability as a reasonable solution concept for this principal-agent matching market by proposing a simple mechanism in which each of the agents proposes a contract and each principal chooses an agent. We show that the equilibrium outcomes of this mechanism coincide with the set of stable outcomes of the matching market.