RENEGOTIATION IN SINGLE-PERIOD SETTINGS
16.3.3 Pre-contract Information
Agent risk aversion plays a key role in most of the models examined in this book. However, in pre-contract information models it is common to assume that the agent is risk neutral.^ In this setting, the principal cannot achieve first-best by selling or renting the firm to the agent since the efficient selling price varies with the agent's information. To induce the agent to accept the contract and communicate his information, the menu must be such that the agent earns information rents (i.e., his expected compensation exceeds his reservation wage) unless he has the worst possible information.
Imperfect Private Information
While communication can be valuable if the agent's private information is imperfect with respect to the outcome, this need not be the case if the agent is risk neutral. This is illustrated in Section 23.3 in a setting in which the number of possible outcomes is at least as large as the number of possible private sig- nals, and a spanning condition is satisfied. An example is used to illustrate this point, and to then illustrate that spanning is not sufficient if the agent is risk averse.
Mechanism Design Problems
In the models discussed above the cost of an agent's action is common knowl- edge, but there is uncertainty about the outcome that will result. Private pre- contract information affects the agent's belief about the likelihood of the out- come resulting from his action choices. In mechanism design problems the agent chooses the outcome, but is uncertain about the cost he will incur in pro- ducing the chosen outcome. His private pre-contract information affects the agent's beliefs about the cost he will incur.
The initial section on mechanism design problems discusses model assump- tions that are sufficient to yield a contract that induces an outcome function that is monotonically increasing with respect to the agent's private information.
^ At the time of contracting, the agent is an informed player and the principal is uninformed.
We assume that the uninformed principal offers a contract, or a menu of contracts, to the in- formed agent. Hence, the analysis is significantly different than in signaling games (see Chapter 13 of Volume I) in which the informed agent offers a contract to the uninformed principal.
This is followed by an analysis of a setting in which there is a positive probabil- ity the agent is not informed, after which we consider a setting in which the agent endogenously decides whether to become informed prior to contracting.
Impact of a Public Report on Resource Allocation
Section 23 A A discusses a mechanism design model that is used to explore the impact of public and private information on investment decisions. In the basic model with no public report, the principal supplies capital to the agent in return for some contracted outcome level. The amount of capital required to produce a given outcome level is equal to the outcome times a random fraction that is revealed to the agent prior to contracting. The agent personally retains the difference between the capital supplied and the capital used. The optimal contract is characterized by a "hurdle" such that if the reported investment cost parameter is greater than the hurdle, zero capital is provided. On the other hand, if the agent reports a cost parameter below the hurdle, the capital provided equals the amount required to produce the maximum output if the cost parame- ter equals the hurdle.
The analysis then introduces a public report that is received prior to the agent receiving his private signal (and before he selects from the menu of con- tracts). The information system partitions the set of possible private signals, reducing the set of possible private signals the agent might receive. This re- duces the expected information rent the principal will have pay to the agent and increases the set of signals for which the principal induces positive investment.
Therefore, the public information generally has positive value to the principal, but negative value to the agent.
The latter result differs from the reporting of public information in a post- contract, pre-decision information setting. In that case the principal is often better off with the public report, but the agent is indifferent since he will reject the contract if he does not expect to receive his reservation utility.
Early versus Delayed Reporting of Private Information
Section 23.4.5 uses a mechanism design model to explore the impact of the agent's report to the principal in a setting in which the agent receives imperfect information before contract acceptance followed later by the receipt of perfect information. The analysis is similar to the analysis of the timing of reports in a post-contract, pre-decision information model in Section 22.7. The principal strictly prefers to receive an early report, but there is a loss in social welfare because the expected reduction in the agent's information rents more than off- sets the principal's expected gain. We again use an example to provide insights into the factors that yield the key results.
163A Intra-period Renegotiation
In Chapters 22 and 23, the agent receives private pre-decision information. In the former, the agent receives the information after contracting and cannot quit the firm after observing his private signal. In the latter, the agent either receives the information prior to contracting or can quit after observing his signal.
Hence, the differences in the two chapters illustrate the impact of differences in commitment to a contract. Chapter 24 explores the impact of other commitment limitations in single-period models.
Most agency theory models assume that the principal and the agent cannot make a mutually acceptable change in (i.e., renegotiate) the contract after it has been signed. However, it is frequently the case that the principal and agent will prefer to renegotiate the contract after the agent has taken his action if the original contract was based on the assumption of no renegotiation. Furthermore, the ability to renegotiate often makes the principal worse off, from an ex ante perspective, which is why it is often exogenously precluded.
Renegotiation-proof Contracts
Section 24.1 considers a standard single-period agency model, but with the added dimension of contract renegotiation after the agent has taken his action.
If a risk neutral principal conjectures that a risk and effort averse agent has been induced to take some specific action, then after the action has been taken, there will be an ex post Pareto improvement if the principal agrees to pay the agent a fixed amount in return for absorbing all of the agent's incentive risk. Of course, if this is anticipated by the agent, he will take his least cost action, and if this is anticipated by the principal, then the initial contract will be a fixed amount that is sufficient to compensate the agent for his least cost action. Con- sequently, the inability to exogenously preclude renegotiation makes the princi- pal worse off
Section 24.1 considers a renegotiation-proof contract that contains a menu from which the agent chooses after he has taken his action. The contract is designed to induce the agent to take a randomized action strategy and the menu is designed to induce him to truthfully reveal his action choice. Hence, the contract is similar to the pre-decision contracts in Chapters 22 and 23, and is also similar to the signaling contracts considered in Chapter 13 of Volume I.
Agent-reported Outcomes
Section 24.2 extends the analysis to consider a sequence of two actions with contract renegotiation between the first action and the first outcome, which precedes the second action and second outcome. In the basic setting, the two outcomes are contractible information and the agent is induced to randomly choose his first action and then reveal his action by his choice from a menu of contracts (as in Section 24.1). The analysis is then extended to consider a set-
ting in which the agent issues unverified reports of the period-specific out- comes, subject to the constraint that the total reported for the two periods cannot exceed the actual total (i.e., there is a limited audit). Interestingly, with agent reporting, there exists a renegotiation-proof contract that does not involve ran- domized first-period actions. Furthermore, the principal strictly prefers to contract on agent-reported outcomes with a limited audit instead of fully audited outcome reports.
Renegotiation Based on Non-contractible Information
Renegotiation can be beneficial if it takes place after the principal has observed the agent's action or after the principal and agent have observed an imperfect signal about the agent's action. This benefit holds even if the principal's obser- vations are not contractible. In fact, the principal can achieve the first-best result if there is anticipated renegotiation after he makes a non-contractible observation of the agent's action. The key to this result is that the principal can offer to replace the agent's incentive contract with a fixed payment that accu- rately reflects the agent's information about the forthcoming compensation.
Hence, in the end, the agent bears no incentive risk.
Principalis Privately Informed
The analysis in Section 24.3 assumes both the principal and the agent make a non-contractible observation of the imperfect performance measure. In Section 24.4, only the principal makes this observation. Renegotiation is now replaced with a menu of contracts which is used to induce the principal to truthfully reveal his private information. In this setting, incentive issues are associated with both the principal and the agent, and the budget balancing constraint restricts the effectiveness of the incentives. To "break" this constraint, a risk neutral third party is introduced.
Resolving a Double Moral Hazard Problem
Chapter 24 concludes by considering a simple model in which both the risk neutral principal and the risk averse agent take personally costly non-contract- ible actions. There are no contractible performance measures. However, the ownership of the firm is tradeable and the principal observes the agent's action.
In this setting, the principal offers the agent a contract that specifies a wage and a buyout price, with the stipulation that after the principal observes the agent's action, the principal will choose whether to retain ownership and pay the agent the wage or sell the ownership to the agent for the buyout price. Interestingly, despite the fact there are no contractible performance measures, the principal can achieve the first-best result.