Optimal Delegation

We analyse the design of decision rules by a principal who faces an informed but biased agent and who is unable to commit to contingent transfers. The contracting problem reduces to a delegation problem in which the principal commits to a set of decisions from which the agent chooses his preferred one. We characterize the optimal delegation set and perform comparative statics on the principal's willingness to delegate and the agent's discretion. We also provide conditions for interval delegation to be optimal and show that they are satisfied when the agent's preferences are sufficiently aligned. Finally, we apply our results to the regulation of a privately informed monopolist and to the design of legislatives rules.     

多层科层中的最优序贯授权与"一刀切"政策

沿袭Tirole(1986)的委托人一中间人一代理人科层结构,本文研究了当委托人不能直接管理代理人时的最优序贯授权问题。在该授权博弈中,委托人通过审慎设计中间人职权范围,影响其对代理入的授权行为,从而激励代理人更有效地提供和使用信息。我们发现,当下属之间利益偏差方向一致时,即中间人较委托入更愿意扩大代理人权限时,采用文献中常关注的“区间授权”(Holm—strom,1977)形式,委托人可以实现其直接向代理人授权时的最优结果。但是,如果下属间利益偏差方向相反,即中间人希望减小代理人权限时,“区间授权”将不再是最优。为了更好地影响控制中间人向代理人的次第授权行为,在最优序贯授权方案中委托人将移除部分中间选项。移除选项数目的多少取决于中间人的利益偏差程度。同授权与激励方面的文献不同,本文表明,即使在信息结构给定的条件下,移除中间项将作为科层中的控制工具,成为最优授权方案的一个特征。本文的发现从激励和授权角度对现行的一些法规执行实践中的“一刀切”政策(比如,“醉驾入刑”、大学招生录取等)提供了一些解释。     

The Economics of Clear Advice and Extreme Options

I study a principal–agent model in which the agent collects information and then chooses a verifiable action. I show that the principal can find it desirable to constrain the agent's action set even though there is no disagreement about the ranking of actions ex post . The elimination or penalization of „intermediate” actions, which are optimal when information is poor, improves incentives for information collection. I characterize optimal action sets when the agent is infinitely risk averse with respect to income shocks and optimal incentive schemes when the agent is risk neutral.     

多层科层中的最优序贯授权与"一刀切"政策

沿袭Tirole(1986)的委托人-中间人-代理人科层结构,本文研究了当委托人不能直接管理代理人时的最优序贯授权问题。在该授权博弈中,委托人通过审慎设计中间人职权范围,影响其对代理人的授权行为,从而激励代理人更有效地提供和使用信息。我们发现,当下属之间利益偏差方向一致时,即中间人较委托人更愿意扩大代理人权限时,采用文献中常关注的"区间授权"(Holmstrom,1977)形式,委托人可以实现其直接向代理人授权时的最优结果。但是,如果下属间利益偏差方向相反,即中间人希望减小代理人权限时,"区间授权"将不再是最优。为了更好地影响控制中间人向代理人的次第授权行为,在最优序贯授权方案中委托人将移除部分中间选项。移除选项数目的多少取决于中间人的利益偏差程度。同授权与激励方面的文献不同,本文表明,即使在信息结构给定的条件下,移除中间项将作为科层中的控制工具,成为最优授权方案的一个特征。本文的发现从激励和授权角度对现行的一些法规执行实践中的"一刀切"政策(比如,"醉驾入刑"、大学招生录取等)提供了一些解释。     

Strategic obscurity in the forecasting of disasters

A principal acquires information about a shock and then discloses it to an agent. After the disclosure, the principal and agent each decide whether to take costly preparatory actions that yield mutual benefits but only when the shock strikes. The principal maximizes his expected payoff by ex ante committing to the quality of his information, and the disclosure rule. We show that even when the acquisition of perfect information is costless, the principal may optimally acquire imperfect information when his own action eliminates the agent's incentive to take action against the risk.     

Why it Pays to Conceal: On the Optimal Timing of Acquiring Verifiable Information

Abstract. We consider optimal contracts when a principal has two sources to detect bad projects. The first one is an information technology without agency costs (IT_P), whereas the second one is the expertise of an agent subject to moral hazard, adverse selection and limited liability (IT_A). First, we show that the principal does not necessarily benefit from access to additional information and thereby may prefer to ignore it. Second, we discuss different timings of information release, i.e., a disclosure contract offered to the agent after the principal announced the result of IT_P , and a concealment contract where the agent exerts effort before IT_P is checked. We find that concealment is superior whenever the quality of IT_P is sufficiently low. Then, IT_P is almost worthless under a disclosure contract, while it can still be exploited to reduce the agent's information rent under concealment. If the quality of IT_P improves, disclosure can be superior as it allows to adjust the agent's effort to the updated expected quality of the project. However, even for a highly informative IT_P , concealment can be superior as it mitigates the adverse selection problem.     

Optimal use of correlated information in mechanism design when full surplus extraction may be impossible

We study the mechanism design problem when the principal can condition the agent's transfers on the realization of ex post signals that are correlated with the agent's types. Crémer and McLean [Econometrica 53(1985) 345-361; 56(1988) 1247-1257], McAfee and Reny [Econometrica 60(2)(1992) 395-421], and Riordan and Sappington [J. Econ. Theory, 45(1988) 189-199] studied situations where the signals are such that full surplus can be extracted from every agent type. We study optimal utilization of the signals when there are fewer signals than types and the Riordan and Sappington conditions do not always hold. For some special cases, we show the level of surplus that can be extracted, and identify the agent types who obtain rent.     

Correlated information, mechanism design and informational rents

Crémer and McLean (Econometrica 56 (1988) 1247-1258) obtain a sufficient and necessary condition for full surplus extraction in Bayesian-Nash equilibrium—the rank condition, which McAfee and Reny (Econometrica 60(2) (1992) 395-421) later generalize for continuous type spaces. This paper shows that, if the principal does not know how noisy is the agent's signal—or equivalently, when signals available to an agent can be ranked by Blackwell's informativeness and, an agent's informativeness is independent of others’ information, the rank condition fails to hold. Conversely, when rank condition fails and informational rents are left to an agent, the model can be interpreted as if, the principal were uncertain about the informativeness of the agent's signal.     

Optimal Contracting of Separable Production Technologies

We analyze the class of agency problems with a risk-neutral principal and a risk-averse agent, in which hidden actions and hidden information (on the agent's efficiency) are jointly present. Technological assumptions such as monotonicity of likelihood are no longer sufficient for the optimal contract to be monotone in the sharing rule. We show that these regularity properties obtain for the rather wide class of production technologies that are separable in the agent's inputs. Together with ordinal properties such as monotone differences and affiliation of inputs, separability yields the monotonicity in efficiency of the agent's actions and indirect utility.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

Collusion, Delegation and Supervision with Soft Information

This paper shows that supervision with soft information is valuable whenever supervisors and supervisees collude under asymmetric information and proceeds then to derive an Equivalence Principle between organizational forms of supervisory and productive activities. We consider an organization with an agent privately informed on his productivity and a risk averse supervisor getting signals on the agent's type. In a centralized organization, the principal can communicate and contract with both the supervisor and the agent. However, these two agents can collude against the principal. In a decentralized organization, the principal only communicates and contracts with the supervisor who in turn sub-contracts with the agent. We show that the two organizations achieve the same outcome. We discuss this equivalence and provide various comparative statics results to assess the efficiency of supervisory structures.     

Dynamic Optimal Taxation with Private Information

We study dynamic optimal taxation in a class of economies with private information. Optimal allocations in these environments are complicated and history-dependent. Yet, we show that they can be implemented as competitive equilibria in market economies supplemented with simple tax systems. The market structure in these economies is similar to that in Bewley (1986) ; agents supply labour and trade risk-free claims to future consumption, subject to a budget constraint and a debt limit. Optimal taxes are conditioned only on two observable characteristics—an agent's accumulated stock of claims, or wealth, and her current labour income. We show that optimal taxes are generally non-linear and non-separable in these variables and relate the structure of marginal wealth and income taxation to the properties of agent preferences.     

Informed principal with correlation

In this paper we analyze an adverse selection model with one principal and one agent, who are both risk neutral and have private information. We assume that the private information of the principal is correlated with that of the agent. The main result of the paper is that the principal can extract a larger share of the surplus from the agent than in the case where her information is public. The principal can design such a contract because she exploits the fact that her type is an informative signal on the agent's one. We fully characterize the equilibrium of the game in which different types of principal offer the same menu of contracts that leaves the agent uninformed about the principal's type. This gives more freedom to the principal when setting the transfers because the agent's constraints need to hold only at an interim stage.     

Individual accountability in teams

We consider a model of team production in which the principal observes only the team output, but agents can monitor one another (at a cost) and provide reports to the principal. We consider the problem faced by a principal who is prevented from penalizing an agent without evidence showing that the agent failed to complete his assigned actions. We show the first-best (high effort but no monitoring) can be achieved, but only if the principal assigns second-best actions. The principal requires monitoring, but agents do not monitor, and as long as output is high, the principal does not penalize agents who fail to monitor. If the principal has the responsibility for monitoring, the first-best outcome cannot be achieved, thus we identify an incentive for delegated monitoring even when agents have no informational advantage.     

Strategic transmission of information and short-term commitment

Summary. We examine the strategic role of information transmission in a repeated principal-agent relationship where the agent produces information that is useful to the principal. The agent values continuous employment for the principal because he makes a relationship-specific investment that can yield rents to him when the relationship is renewed. Assuming that the parties are sufficiently impatient, we show that full disclosure of the information produced occurs early in the relationship when the principal can commit to a long-term relationship, when the agent observes his valuation of continuous employment after making a report on information produced, or when the agent obtains a low valuation of continuous employment before making a report. By contrast, a strategic delay in the transmission of information occurs when the principal can only commit to a short-term relationship and the agent obtains a high valuation of continuous employment before making a report. Received: October 15, 1997; revised version: July 27, 1998     

Discretionary rewards as a feedback mechanism

This paper studies the use of discretionary rewards in a finitely repeated principal–agent relationship with moral hazard. The key aspect is that rewards have informational content. When the principal obtains a private subjective signal about the agent's performance, she may pay discretionary bonuses to provide credible feedback to the agent. In accordance with the often observed compression of ratings, we show that in equilibrium the principal communicates the agent's interim performance imperfectly, i.e., she does not fully differentiate good and bad performance. Furthermore, we show that small rewards can have a large impact on the agent's effort, provided that the principal's stake in the project is small.     

For how long to tie your hands? Stable relationships in an unstable environment

The Kreps–Wilson–Milgrom–Roberts framework is one of the most renowned ways of modeling reputation-building. Once the number of repetitions of the game is considered as a choice variable, such a framework can fruitfully be employed to study the optimal length of the commitment to a relationship. We analyze a model where a principal plays with an agent a finitely repeated trust game, characterize the optimal length of the relationship between principal and agent when the principal’s preferences on the agent’s type stochastically change over time and show that a commitment to a stable relationship may be optimal (even) in very unstable environments.      

Competition between asymmetrically informed principals

Summary. This paper derives the set of equilibria for common agency games in which the principals compete in piece rates and lump sum payments and one principal has incomplete information about the agent's preferences. We show that the uninformed principal's expected payoff function is discontinuous with respect to the identity of the marginal agent type. This discontinuity is shown to support an open set of equilibria. For games in which the first-best equilibrium strategies are measurable with respect to the uninformed principal's information partition, this result implies the existence of an open set of Pareto inefficient equilibria. Received: December 5, 1995; revised version August 18, 1996     

Erratum to “Negotiation and take it or leave it in common agency”: [Journal of Economic Theory 111 (2003) 88-109]

The no-externalities condition provided in the text is not sufficient for Theorems 3 and 4 when effort is not fully contractable. In the case where the principals cannot contract at all on agent's effort, the condition in the text requires that for any set of alternatives offered by the principal there is one that is at least as good as all other alternatives in the set for the agent no matter what the other principal does, no matter what effort the agent takes, and no matter what the agent's type. In fact, a stronger condition is required. For any set of alternatives offered by a principal, each of the choices within this set that is at least as good for the agent as any other choice within the set must remain so no matter what actions the other principals take, no matter what effort the agent takes, and no matter what the agent's type.     

Contracting with Diversely Naive Agents

In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a "cognitive" nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of "sophistication", that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and "exploitative" contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.