Principal - Agent Games. Sometimes asymmetric information develops after a contract has been signed In this case, signaling and screening do not help, since they are only effective at separating types before signing a contract The classic example – an owner of a firm hires a manager and wants the manager to maximize the profits of the firm There are two main sources of asymmetric information (1)the owner cannot observe the manager’s effort (2)the manager might obtain better information about firm’s opportunities than owner Problems of this type are known as principal agent problems - the principal hires the agent and wants the agent to take actions that maximize the principal’s welfare, - but the agent’s preferences might differ from the principal - the agent might be more risk averse and dislike effort

Information problems. The two parties attempt to design a contract that deals with these problems (1)Hidden action – the principal does not observe the agents actions - ex: in the firm, the action is work effort - in insurance, the action is safe driving - this is known as the moral hazard problem (2) Hidden information – the agent acquires better information - ex: new investment opportunities Suppose an owner wants to hire a manager for a one-time project Suppose that the project’s profits are affected by the manager’s actions - if the manager’s actions are observable, both to the owner and to a third party enforcer, then the contract could be quite simple: it would specify the manager’s actions and corresponding wage The contract would be a forcing contract, where the manager is paid only if actions are performed.

Hidden Action. Even if the P and A can observe actions, this is not enough as they must be verifiable by a third party. If the manager’s actions cannot be observed, then the contract cannot specify particular actions, since they cannot be verified. In this case, the manager’s compensation can only be based on observable variables Profits may or may not be observable and verifiable, but we will assume that they are This may be more appropriate for the top managers than anyone else - as they affect the profits of the whole company and these profits might be public - or good proxies like share price are public For regular workers involved in team production, this only provides a rough guide.

Let π denote the project’s profits -observable and verifiable. Let e denote the manager’s effort – usually e is assumed as a one-dimensional real number, - but it could also be a vector If profits are a deterministic function of e and presumably a monotonic function, - then e could be inferred perfectly just by observing profits. This case is then no different from the case where effort can be observed. More realistically, Shocks can affect π -we cannot perfectly infer e f rom observing π Hidden Action Model. e1e1 e π(e)π(e) π π1π1

Shocks.

High profits are more likely with e H.

Manager’s expected utility fn.

Assume that the owner receives the profits minus the wages. - assume that the owner is a risk neutral expected payoff maximizer. - owners can diversify, so they are less risk averse than the manager is Consider a game where, 1- the owner moves first and chooses a contract to offer the manager 2- then the manager observes the contract and either accepts or rejects 3- if the manager accepts, then he chooses an effort level 4- then shocks are realized 5- payoffs are determined. Initially, suppose that effort is observable, then the contract would specify - manager’s effort level and manager’s wage as a function of profits w(π) - Assume that the manager has a reservation utility level. - So the owner must provide manager with an expected utility of at least. - or the manager will not accept the contract.. Owner maximizes net revenue (π-w).

. When effort is observable.

. Transform optimization problem.

. Lagrangian.

Risk Sharing result.

If manager is risk neutral.

When effort is not observable.

Optimal contract w/unobservable effort. We have the following result for the case with unobserved effort. Prop: In the PA model with unobservable effort and a risk neutral A, an optimal contract generates the same effort choice and expected utilities for the manager and the owner as when e is observable. Proof:: Note that the P can always do at least as well when e is observable as when it is not, since the P could always ignore e in choosing a contract. So if we find a contract when e is unobservable that generates the same expected payoffs as the optimal contract when e is observable, then the contract must be optimal. This is the plan.

Risk neutral agent.

Risk adverse agent. The intuition for the prior result is since A is risk neutral, there is no need for risk sharing. - Efficient incentives can be provided by selling the A the firm. - Then the A gets the full marginal return from e. With a risk adverse agent, proceed by taking 2 steps 1) characterize the optimal contract for each effort level 2) choose the effort level to maximize the P’s payoff In solving 1), the P’s problem reduces to the wage minimization problem discussed above; the difference is now there is an added constraint because the contract cannot specify e. The wage function w(π) must be chosen so that when the A chooses e to max - the optimal e is the effort level the P is trying to get A to choose.

So the Principal’s problem is.

Implementing high effort.

Proof that constraints bind.

Optimal contract when P chooses e H.

Likelihood ratio.

Monotone likelihood ratio property. w F 1 f

Principal’s payments.

Summing Up. The wage payment for implementing e L is exactly the same as when effort is observable. The expected wage payment for implementing e H is strictly larger in the non-obs. effort case. So, non-observable effort raises the cost of implementing e H and does not change the cost of implementing e L. This could lead to an inefficiently low level of effort being implemented. When e L is optimal under obs, it is still optimal under non-obs, and non-obs causes no losses. If e H would be optimal under observability, then under non-observability either 1) could still be optimal to implement, but A must bear risk and the expected wage rises 2) the risk bearing costs may be high enough that P decides that it is better to implement e L In either case, non-observability causes a welfare loss to P. - A gets an expected utility equal to his reservation utility no matter what. Note: a social planner can’t improve welfare unless the planner can observe effort when P can’t