RENEGOTIATION IN SINGLE-PERIOD SETTINGS
16.5 MULTIPLE AGENTS IN SINGLE-PERIOD SETTINGS
In Chapters 17 and 18 we focus on single-agent, single-task, single-period agency models. Chapter 20 introduces multiple tasks performed by a single agent in a single period. Then, Chapter 25 through 28 consider multiple tasks performed by a single agent over multiple periods, with a possible change of agent at the end of a period. In Chapters 29 and 30 we very briefly consider some key issues that arise when multiple agents perform multiple tasks within a single period. Chapter 29 considers multiple productive agents, whereas Chapter 30 considers settings in which one agent is productive, while the other is a monitor of the productive agent.
16.5.1 Multiple Productive Agents
We begin Chapter 29 by revisiting the partnership model introduced in Chapter 4 of Volume I. The original model focuses on risk sharing and assumes that either the partners' actions are contractible information or they do not incur any personal costs in taking those actions. Now we assume all partners provide effort that is personally costly and non-contractible. "Budget balancing" and
"free rider" problems occur if the aggregate outcome is the only contractible information. These problems can be partially dealt with by committing to give away some of the aggregate outcome if the performance information indicates that all partners should be penalized. Introducing partner-specific performance measures is also shown to be useful, as is the addition of a general partner who does not provide effort, but provides additional risk sharing capacity and, more importantly, permits the partnership to avoid the "budget balancing" constraint with respect to the productive partners.
In Section 29.2 we move from the partnership interpretation of multiple effort averse agents with an effort neutral general partner to an agency interpre- tation. The general partner is now called a principal. To focus on incentive issues and simplify the risk sharing issues, we assume the principal is both risk
and effort neutral, and offers incentive contracts to risk and effort averse agents who operate the principal's firm. We view the principal as a Stackleberg leader who specifies the payoffs for a subgame played by the agents. If the perform- ance measures are correlated or are jointly affected by the actions of multiple agents, then the incentive compatibility constraints are potentially much more subtle than in single-agent settings. The agents choose their actions in a simul- taneous play game and to be incentive compatible, their action choices must constitute a Nash equilibrium. However, there may be multiple Nash equilibria and the agents' choice may differ from the equilibrium preferred by the princi- pal.
For example, consider a setting in which there are separate action-inform- ative performance measures for two agents. If the performance measures are correlated, then using the measure for one agent as a standard in the contract with the other agent can reduce the incentive risk premia. Assume that the con- tracts are such that one agent finds it optimal to provide high effort if he be- lieves the other agent is providing high effort, i.e., this is a Nash equilibrium.
However, there may be other Nash equilibria which the agents prefer, e.g., both agents provide low effort and claim their poor outcomes are due to bad eco- nomic conditions.
One mechanism for dealing with the joint shirking problem described above is to offer one agent an optimal "single-agent" contract based on his own per- formance measure (so he will not benefit from joint shirking). Then his per- formance measure can be used as a relative performance measure in contracting with other agents.
In the basic multi-agent model (e.g., in Section 29.2), the principal contracts directly with every agent. In Section 29.3 we consider a setting in which the principal contracts with one agent (the branch manager) who in turn contracts with a second agent (the worker). In effect the principal sets the terms of the size of the pie (the compensation pool) and allows the manger to determine how the pie will be divided. This can be viewed as descriptive of either decentra- lized contracting or centralized contracting subject to agent renegotiation or collusion.
In the partnership setting introduced in Chapter 4, in which the partners are risk averse and effort neutral, the efficient partnership contract gives each part- ner a linear share of the total outcome if all partners have HARA utility func- tions with identical risk cautiousness. In that setting, centralized and decentral- ized contracting produce the same results. As established in Chapter 4, in this setting efficient contracts produce congruent preferences among the partners.
In an agency with a risk and effort neutral principal and risk and effort averse agents, the optimal centralized contract will assign all risk to the prin- cipal, except for the incentive risk that is assigned to each agent. A key feature of a decentralized contract is that the risk averse manager will choose to take on some of the worker's incentive risk and to assign some of the manager's incen-
tive risk to the worker. In addition, while the marginal impact of the agents' actions on the principal's payoff plays a central role in the agents' incentive rates chosen by the principal, the manager will ignore the principal's payoff in his contract choice, unless the principal's payoff is also the performance meas- ure used in the agents' contracts. Centralized and decentralized contracting pro- duce identical results if the agents are identical and contracting is based on the principal's aggregate payoff However, more generally, decentralized contracts involve inefficient risk sharing and inefficient allocation of effort among the agents. Nonetheless, the principal may prefer decentralized versus centralized contracting if the manager has "local" information about the worker's perfor- mance that is not available to the principal.
In Section 29.4 we consider settings in which the agents have private pre- contract information. Recall that in Chapter 23 we consider single-agent models with private pre-contract information. In this type of model, the agents can be risk neutral since information rents replace risk premia as the central focus.
Some of the insights generated by the pre-contract information models are similar to insights provided by the basic principal/multi-agent models described above. However, there are differences.
The Revelation Principle applies and the agents are offered menus of con- tracts that induce them to truthfully report their information. The cost incurred by an agent depends on the outcome he produces and an agent-specific state (i.e., the models considered are mechanism design problems). The states are correlated so that it can be optimal to use both agents' outcomes in specifying the compensation for each agent. We consider two formulations of the princi- pal's problem. In the first, the principal is assumed to induce each agent to report truthfully under the assumption the other agent is motivated to report truthfully. In the second, the principal is assumed to induce each agent to report truthfully even if he believes the other agent will lie (i.e., truthful reporting is a dominant strategy). With risk neutrality, it is possible to attain first-best using the two performance measures. However, that is not possible if the agents are risk averse, since the agents must bear risk, for which they are compensated.
If the states are correlated, then subgame issues arise in this setting just as they did in the basic multi-agent model. Care must be taken specifying the truth- telling constraints. It is not sufficient to require truth-telling to be an optimal response given that the other agent is telling the truth. The principal must also ensure that the agents cannot benefit by colluding in what they report. Similarly to the basic multi-agent model, one way to accomplish this is to offer one agent a contract in which truthful reporting is an undominated strategy, and then use his truthful report in contracting with the other agent.
16.5.2 A Productive Agent and a Monitor
In the final chapter of the book, we introduce a monitor (e.g., a supervisor or an auditor) as an agent who provides information that is useful in contracting with a productive agent. Our coverage is relatively brief, and is restricted to models in which the principal offers outcome- and report-contingent contracts to both the monitor and the productive agent. Hence, we do not consider settings in which the auditor's incentives stem from threats of litigation or from reputation effects, i.e., we consider internal auditors as opposed to external auditors hired on a fixed fee basis.
In the models considered in this chapter, the cost of the worker's action (e.g., the output produced) is random and the worker has private pre-contract information with respect to his cost. Hence, the models are similar to the models in the mechanism design problems considered in Section 23.4. As in Chapter 23, the privately informed worker earns information rents if he has
"good news". The key difference is the introduction of an internal monitor who reports private information he obtains about the agent's information, which is used to reduce information rents (and improve production efficiency). In these settings both the worker and the monitor are induced to truthfully report their private information. As in the prior chapter, care must be taken in specifying the incentive compatibility constraints. The contracts induce each agent to report truthfully and to take the actions desired by the principal, considering both unilateral choices by each agent and coordinated actions by the two agents.
In this chapter we introduce indirect mechanisms for dealing with the sub- game issues associated with coordinated actions by the two agents. Section 30.1 considers a basic model in which there is an informed worker and a costly monitor. The cost of the worker's action is affected by a random state variable, which he observes. The monitor can also observe the state, but only if he incurs a cost. An indirect ("whistle blowing") mechanism is introduced for inducing the worker to report truthfully and for inducing the monitor to incur the infor- mation cost and report truthfully. The monitor reports first and then the worker has three choices: accept, reject, or counter-propose (with apre-specified "side- bet"). In equilibrium, the monitor will acquire the information and report truth- fully, and then the worker will accept the contract. With risk neutrality, this mechanism can achieve first-best.
The preceding model is extended to a setting in which the monitor's infor- mation is imperfect - it partitions the worker's information. An indirect "whis- tle blowing" mechanism is again used, but does not achieve first-best.
Section 30.2 considers variations on a model in which the worker has perfect information about the state that influences the costs he will incur in producing a given level of output and the monitor can obtain imperfect informa- tion about the state. Both agents are risk neutral and have limited liability (i.e., there is a lower bound on the compensation they can receive). Two benchmark
cases are considered, one has a perfect monitor and the other has no monitor.
No information rent is paid and the output is efficient if the monitor is perfect, whereas information rent and inefficient output are used to motivate the worker if there is no monitor. Extensive analysis is then provided for a model in which the monitor's information is costless (he is employed for other purposes) but im- perfect, and he will report truthfully because he has no incentive to lie. The worker is induced to produce a high output in the good state and low (possibly inefficient) output in the bad state, and the monitor is instructed to obtain and report his imperfect information if the worker produces the low output. The worker receives a base pay for the output produced and is penalized for a low output if the monitor makes a type II error (i.e., the principal incorrectly rejects the worker's claim that his low output is due to a bad state). The worker must be compensated for the expected cost of this incorrect penalty, but using a penalty based on the monitor's imperfect report allows the principal to reduce (and possibly eliminate) the information rent and increase the low output level that are used to motivate the worker's effort. Comparative statics provide insights into how the quality of the monitor's information affects the low pro- ductivity output and the information rent received by the worker if he has good news. Two measures of information quality are considered. One assumes there are no type II errors and varies the probability of type I errors (i.e., erroneously accepting a claim by the worker that his low output is due to a bad state). The other measure of quality assumes the errors are symmetric, i.e., both types of error are equally likely. Interestingly, in both settings, first-best results can be achieved with less than perfect information. Of course, the risk neutrality of the worker is crucial for this result. Also, the size of the penalty that can be im- posed affects the quality of the information necessary to achieve first-best.
We define collusion to involve side-payments between agents for the pur- pose of inducing coordinated actions that differ from the actions that would be induced by a contract if there were no side-payments. Hence, collusion goes beyond the coordinated actions that created the subgame problems discussed in Chaper 29. Of course, as stated earlier, delegated contracting (see Section 29.3) can be viewed as equivalent to a model with collusion.
The impact of collusion between the worker and the monitor is explored in Sections 30.2.3 and 30.2.4. We refer to a monitor as collusive if there is a potential for collusion. The fact that a monitor is collusive does not mean col- lusion occurs. Recall that in settings where contract renegotiation is possible, it does not occur if the principal offers a renegotiation-proof contract (see Chapters 24 and 28). Similarly a collusive monitor will not engage in collusion if the principal offers a collusion-proof contract. Nonetheless, as the analysis demonstrates, collusiveness can destroy the value of the monitor, partially reduce his value, or have zero impact on his value. As we demonstrate, there are three factors that affect the loss of value due to collusiveness. The first is the set of feasible lies the monitor can tell. The second is the restrictiveness of
the monitor's limited liability. The third is the probability of a type II error - is it positive or zero?
Two types of mechanisms for controlling collusion are considered: a reward option and a penalty option. In our example, if the principal ignores the possi- bility of collusion, then the manager will bribe the monitor not to issue a report that would result in the manager being penalized. The principal can counter this collusion by offering a reward to the monitor for issuing a negative report.
The chapter, and the book, concludes with a model in which a costly exter- nal monitor (with exogenous incentives, e.g., the threat of litigation or loss of reputation) is hired to audit the report of a costless, collusive internal monitor (whose collusiveness is costly to the principal). The external monitor is only hired with positive probability if the worker's outcome is low and the internal monitor accepts the worker's claim that his low outcome is due to a poor state.
The manager and internal monitor are penalized if the external monitor reveals that the internal monitor lied.