Incentive problems arise when a principal wants to delegate a task to an agent. Delegation can be motivated either by the possibility of benefitting from some increasing returns associated with the division of tasks, which is at the root of eco- nomic progress, or by the principal’s lack of time or lack of any ability to perform the task himself, or by any other form of the principal’s bounded rationality when facing complex problems. However, by the mere fact of this delegation, the agent may get access to information that is not available to the principal. The exact opportunity cost of this task, the precise technology used, and how good the match- ing is between the agent’s intrinsic ability and this technology are all examples of pieces of information that may become private knowledge of the agent. In such cases, we will say that there is adverse selection.
The agency model analyzed in this chapter, as well as in most of the book, will be cast in terms of a manager-worker relationship. Examples of such agency relationships under adverse selection abound both in terms of their scope and their economic significance. Both private and public transactions provide examples of contracting situations plagued with informational problems of the adverse selec- tion type. The landlord delegates the cultivation of his land to a tenant, who will be the only one to observe the exact local weather conditions. A client delegates his defense to an attorney who will be the only one to know the difficulty of the case. An investor delegates the management of his portfolio to a broker, who will privately know the prospects of the possible investments. A stockholder delegates the firm’s day-to-day decisions to a manager, who will be the only one to know the business conditions. An insurance company provides insurance to agents who privately know how good a driver they are. The Department of Defense procures a good from the military industry without knowing its exact cost structure. A reg- ulatory agency contracts for service with a Public Utility without having complete information about its technology…
The key common aspect of all those contracting settings is that the informa- tion gap between the principal and the agent has some fundamental implications for the design of the bilateral contract they sign. In order to reach an efficient use of economic resources, this contract must elicit the agent’s private informa- tion. This can only be done by giving up some information rent to the privately informed agent. Generally, this rent is costly to the principal. This information cost just adds up to the standard technological cost of performing the task and justifies distortions in the volume of trade achieved under asymmetric information. The allocative and the informational roles of the contract generally interfere. At the optimal second-best contract, the principal trades off his desire to reach allocative efficiency against the costly information rent given up to the agent to induce infor- mation revelation. Under adverse selection, the characterization of the volume of trade cannot be disentangled from the distribution of the gains from trade.
This chapter analyzes the contractual difficulties that appear when this dele- gation of task takes place in a one-shot relationship. The fact that the relationship is one-shot means that the principal and the agent cannot rely on its repetition to achieve efficient trades.2 In this case, the bilateral short-term relationship between the principal and the agent can be regulated only by a contract. Implicit here is the idea that there exists a legal framework for this contractual relationship. The contract can be enforced by a benevolent court of law, and the agents are bound by the terms of the contract. This implicit assumption on the legal framework of trades is not peculiar to contract theory but prevails in most traditional studies of market economies.
The main objective of this chapter is to characterize the optimal rent extraction-efficiency trade-off faced by the principal when designing his contrac- tual offer to the agent. This characterization proceeds through two steps. First, we describe the set of allocations that the principal can achieve despite the information gap from which he suffers. An allocation is an output to be produced and a distribution of the gains from trade. Even under adverse selection, those allocations can be easily characterized once one has described a set of incentive compatibility constraints that are only due to asymmetric information. In addition to those constraints, the conditions for voluntary trade require that some participa- tion constraints also be satisfied to ensure that the agent wants to participate in the contract. Incentive and participation constraints define the set of incentive feasible allocations. Second, once this characterization is achieved, we can proceed to a normative analysis and optimize the principal’s objective function within the set of incentive feasible allocations. In general, incentive constraints are binding at the optimum, showing that adverse selection clearly impedes the efficiency of trade. The main lessons of this optimization are that the optimal second-best contract calls for a distortion in the volume of trade away from the first-best and for giving up some strictly positive information rents to the most efficient agents.
Implicit in this optimization are a number of assumptions worth stressing. First, we assume that the principal and the agent both adopt an optimizing behav- ior and maximize their individual utility. In other words, they are both fully ratio- nal individualistic agents. Given the contract he receives from the principal, the agent maximizes his utility and chooses output accordingly. Second, the principal does not know the agent’s private information, but the probability distribution of this information is common knowledge. There exists an objective distribution for the possible types of the agent that is known by both the agent and the prin- cipal, and this fact itself is known by the two players.3 Third, the principal is a Bayesian expected utility maximizer. In designing the agent’s payoff rule, the principal moves first as a Stackelberg leader under asymmetric information antic- ipating the agent’s subsequent behavior and optimizing accordingly within the set of available contracts.
Section 2.1 describes the adverse selection canonical model that we use in most of this book. For the sake of simplicity, we assume that the agent’s type, i.e., his cost parameter, can only take two possible values. The discrete type model turns out to be sufficient to highlight the main phenomena arising under adverse selection without having to deal with the technicalities of a continuum of types.4 In section 2.2, we provide the benchmark solution corresponding to the case where the principal knows perfectly the agent’s cost function. Section 2.3 describes the set of allocations that the principal can achieve despite the information gap from which he suffers. Section 2.4 explains why the principal is generally obliged to give up an information rent to the agent because of the latter’s informational advantage. The optimization program of the principal who wants to maximize his expected utility under the constraints of incentive compatibility and voluntary trade is described in section 2.5. The optimal contract of the principal is obtained and discussed in section 2.6. Two major illustrations are given in sections 2.7 and 2.8. Section 2.9 proves the revelation principle in the principal-agent setup. This principle guarantees that there is no loss of generality in restricting the anal- ysis to menus of two contrats when the agent’s private cost information takes only two possible values. The analysis of the previous sections is then extended to more general cost and revenue functions in section 2.10. This allows us to illustrate new features of the rent extraction-efficiency trade-off. So far, the analysis assumed risk neutrality of the agent and an interim timing of contracting, i.e., the principal offers a contract to an agent once the latter has already learned his type. Sec- tion 2.11 considers the more symmetric case where the contract can be offered at the ex ante stage, i.e., before the agent learns his type. We perform this analysis under various assumptions on the degrees of risk aversion of the principal and the agent. Implicit in our whole analysis of this chapter is the assumption that the agent and the principal can commit to the terms of the contract. This assumption is discussed in section 2.12. Section 2.13 gives a closer look at the set of incen- tive feasible allocations and in particular at the convexity of this set. We show there the conditions under which stochastic mechanisms can be useful for the principal. Given that the principal suffers from an information gap with the agent, informative signals can be useful for improving contracting and the terms of the rent extraction-efficiency trade-off. Section 2.14 studies the added value of these informative signals. Finally, in section 2.15, we present many examples of con- tracting relationships highlighting the generality of the framework provided in this chapter.
Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.