Stochastic Mechanisms

We consider here the framework of section 2.10 with a general cost function C(q, θ).  Let  us  rewrite  the  principal’s  problem  as When  S(·) is  concave  and  C(·) is  convex,  the  principal’s  objective  function is  concave  in .  Neglecting  constraints  (2.78)  and  (2.79)  as  usual,  the remaining constraints (2.77) and (2.80) define a convex

Informative Signals to Improve Contracting

In this section, we investigate the impacts of various improvements of the prin- cipal’s information system on the optimal contract. The idea here is to see how signals that are exogenous to the relationship can be used by the principal to bet- ter design the contract with the agent. The simple observation of performances

Contract Theory at Work

This section proposes several classical settings where the basic model of this chap- ter is useful. Introducing adverse selection in each of these contexts has proved to be a significative improvement of standard microeconomic analysis. 1. Regulation  In the Baron and Myerson (1982) regulation model, the principal is a regulator who maximizes a weighted

Incentive and Participation Constraints with Adverse Selection

The main theme of chapter 2 was to determine how the fundamental conflict between rent extraction and efficiency could be solved in a principal-agent rela- tionship with adverse selection. In the models presented in chapter 2, this conflict was relatively easy to understand because it resulted from the simple interaction of a single incentive

Adverse Selection: More than Two Types

Suppose  that  h may  take  three  possible  values,  i.e., ,  with  θ¯ − θˆ = θˆ − θ = Δθ for simplicity, and with respective probabilities v, vˆ, and v¯ such that v + vˆ + v¯ = 1. We denote a truthful direct revelation mechanism in this three-type environment  by .  Using  similar

Adverse Selection: Multidimensional Asymmetric Information

Another important limitation of our analysis of adverse selection in chapter 2 is that the adverse selection parameter h was modeled as a unidimensional parameter. In many instances, the agent simultaneously knows several pieces of information that are payoff relevant and affect the optimal trade. For instance, a tax authority would like to know

Adverse Selection: Type-Dependent Participation Constraint and Countervailing Incentives

The models in sections 3.1 and 3.2 have already illustrated the difficulties that the modeler faces when there is no obvious order between the various incen- tive constraints. The same kind of difficulties arise when the agent’s participa- tion constraint is type-dependent. Indeed, those participation constraints may also perturb the natural ordering of the

Adverse Selection: Random Participation Constraint

The previous section has shown how a deterministic but type-dependent participa- tion constraint could perturb the standard results on the optimal rent extraction- efficiency trade-off. We now perturb the agent’s participation constraint in another direction, by allowing some randomness in the decision to participate. Instead of the agent’s reservation utility being perfectly known, let

Adverse Selection: Limited Liability

Sometimes the set of incentive-feasible contracts is constrained by some exogenous limits on the feasible transfers between the principal and the agent. These exoge- nous financial constraints could reveal the existence of previous financial contracts that the agent might have already signed. Those constraints will of course affect the usual rent-efficiency trade-off. A first

Adverse Selection: Audit Mechanisms and Costly State Verification

Sometimes the principal would like to relax the efficient type’s incentive constraint by making it somewhat costly for him to lie and claim that he is inefficient. One important way to do so is by using an audit technology that can detect the agent’s nontruthful report and allows for some punishment when a false

Adverse Selection: Redistributive Concerns and the Efficiency-Equity Trade-Off

In the rent extraction-efficiency trade-off analyzed so far, the principal wants to minimize the information rent left to the agent for a given level of output. The principal has no redistributive concerns vis-à-vis the agent. In the optimal tax-ation literature, starting with the seminal paper of Mirrlees (1971), the principal (generally a government or

Moral Hazard: The Basic Trade-Offs

In chapter 2, we stressed that the delegation of tasks creates an information gap between the principal and his agent when the latter learns some piece of informa- tion relevant to determining the efficient volume of trade. Adverse selection is not the only informational problem one can imagine. Agents to whom a task has

Moral Hazard: The Model

1. Effort and Production  We consider an agent who can exert a costly effort e. Two possible values can be taken by e, which we normalize as a zero effort level and a positive effort of one: e  in  {0, 1}.  Exerting  effort  e  implies  a  disutility  for  the  agent  that  is  equal  to 

Moral Hazard: Risk Neutrality and First-Best Implementation

If the agent is risk-neutral, we can assume that (up to an affine transformation) u(t) = t for all t and h(u) = u for all u. The principal who wants to induce effort must thus choose the contract that solves the following problem: With risk neutrality the principal can, for instance, choose incentive compat-ible transfers

Moral Hazard: The Trade-Off Between Limited Liability Rent Extraction and Efficiency

Let us consider a risk-neutral agent. As we have already seen, (4.3) and (4.4) now take the following forms: Let us also assume that the agent’s transfer must always be greater than some exogenous level −l, with l ≥ 0. The framework is quite similar to that of section 3.5, and we refer the

Moral Hazard: The Trade-Off Between Insurance and Efficiency

Let us now turn to the second source of inefficiency in a moral hazard context— the agent’s risk aversion. When the agent is risk-averse, the principal’s program is written as: It is not obvious that kP l is a concave program for which the first-order Kuhn and Tucker conditions are necessary and sufficient. The

Moral Hazard: More than Two Levels of Performance

We now extend our previous 2 × 2 model to allow for more than two levels of performance. We consider a production process where n possible outcomes can be realized. Those performances can be ordered so that q1 < q2 < ··· < qi < ··· < qn. We denote the principal’s return in each

Moral Hazard: Informative Signals to Improve Contracting

As in the case of adverse selection analyzed in section 2.14, various verifiable signals can be used by the principal to improve the provision of incentives to the agent in a moral hazard framework. These pieces of information can be gathered by different kinds of information systems that are internal to the organization in

Moral Hazard: Moral Hazard and the Theory of the Firm

The trade-off between risk and incentives provides one possible explanation of the wage compensations used in firms.19 The widespread use of stock options for CEOs can be seen as a result of the desire of the firm’s owners to let these agents bear more risk so that they are better incentivized.20 Similarly, the use

Moral Hazard: Contract Theory at Work

This section elaborates on the moral hazard paradigm discussed so far in a number of settings that have been discussed extensively in the contracting literature. 1. Efficiency Wage  Let us consider a risk-neutral agent working for a firm, the principal. By exerting effort e in f0h 1i, the firm’s added value is V¯ (resp. V