Changing One's Mind when the Facts Change: Incentives of Experts and the Design of Reporting Protocols

Experts often collect and report information over time. What reporting protocol elicits the most information? Here, a principal receives reports sequentially from an agent with privately known ability, who observes two signals about the state of the world. The signals differ in initial quality and, unlike previous work, differ in quality improvement . The paper finds that "mind changes" (inconsistent reports) can signal talent if a smart agent improves faster. Also, sequential reports dominate when the principal's decision is very sensitive to information; a single report dominates if the mediocre agent's signals improve faster or the agent is likely mediocre.
When the facts change, I change my mind. What do you do, sir? — John M. Keynes ¹     

Bayesian consistent belief selection

A subjective expected utility agent is given information about the state of the world in the form of a set of possible priors. She is assumed to form her beliefs given this information. A set of priors may be updated according to Bayes' rule, prior-by-prior, upon learning that some state of the world has not obtained. In a model in which information is completely summarized by this set of priors, we show that there exists no decision maker who obeys Bayes' rule, conditions her prior only on the available information (by selecting a belief in the announced set), and who updates the information prior-by-prior using Bayes' rule.     

INFORMATION GATHERING BY A PRINCIPAL*

In the standard principal–agent model, the information structure is fixed. In this article the principal can choose to acquire additional information about the state of the world before he contracts with an agent. In the event that the principal acquires this information, the agent never learns what the principal knows about the state of the world. I examine cases where the agent can and cannot observe whether the principal has acquired the additional information. The implications for risk sharing, information acquisition, investment, and welfare are examined for both cases.     

Collusion and Renegotiation in a Principal–Supervisor–Agent Relationship

We describe a principal–supervisor–agent relationship in which agent and supervisor may collude. To prevent collusion, the principal may contract on a noisy signal which is correlated with the occurrence of collusion. When the signal is informative enough, the principal uses it and no collusion occurs in equilibrium. These contracts, however, are ex post inefficient and are only optimal if the principal can commit not to renegotiate. With renegotiation it is never optimal for the principal to prevent collusion and, at the same time, condition contracts on the signal. In fact, when the signal is informative enough collusion occurs in equilibrium.     

Asymmetric awareness and moral hazard

This paper introduces asymmetric awareness into the classical principal–agent model and discusses the optimal contract between a fully aware principal and an unaware agent. The principal enlarges the agentʼs awareness strategically when proposing a contract and faces a tradeoff between participation and incentives. Leaving the agent unaware allows the principal to exploit the agentʼs incomplete understanding of the world, relaxing the participation constraint, while making the agent aware enables the principal to use the revealed contingencies as signals about the agentʼs action choice, relaxing the incentive constraint. The optimal contract reveals contingencies that have low probability but are highly informative about the agentʼs effort.     

Contracts and Productive Information Gathering

We modify a standard Baron–Myerson model by assuming that, instead of knowing the state of nature, the agent has to incur a cost γ to learn it. Under these conditions, the principal will offer contracts that, depending on the value of γ, try to induce the agent to gather or not to gather information. We study the tradeoffs that are involved.Journal of Economic LiteratureClassification Numbers: D82, D83.     

Communication in bargaining over decision rights

This paper develops a model of bargaining over decision rights between an uninformed principal and an informed but self-interested agent. We introduce two different bargaining mechanisms: tacit and explicit bargaining. In tacit bargaining, an uninformed principal makes a take-it-or-leave-it price offer to the agent, who then decides whether to accept or reject the offer. In the equilibrium of the game, the principal inefficiently screens out some agent types so that the agent's private information cannot be fully utilized when the decision is made. In explicit bargaining in which parties can communicate explicitly via cheap talk before tacit bargaining, however, an equilibrium with no such inefficient screening exists even when the conflict of interest is arbitrarily large. We also follow a mechanism design approach, showing that under certain conditions, explicit bargaining is an optimal bargaining mechanism that maximizes the joint surplus of the parties.     

Task assignment under agent loss aversion

We analyze a task-assignment model in which a principal assigns a task to one of two agents depending on future states. If the agents have concave utility, the principal assigns the task to them contingent on the state. We show that if the agents are loss averse, a state-independent assignment–assigning the task to a single agent in all states–can be optimal even when the principal can write a contingent contract at no cost.     

Optimal limited authority for principal

This article studies a principal-agent problem where the only commitment for the uninformed principal is to restrict the set of decisions she makes following a report by the informed agent. We show that an ex ante optimal equilibrium for the principal corresponds to a finite partition of the state space, and each retained decision is ex post suboptimal for the principal, biased toward the agent?s preference. Generally an optimal equilibrium does not maximize the number of decisions the principal can credibly retain. Compared to no commitment, limited authority improves the quality of communication from the agent. As a result, it can give the principal a higher expected payoff than delegating the decision to the agent.     

Rank-order tournaments and selection

Rank-order tournaments are often presented as devices for aligning incentives in a principal-agent setting. In most of this literature agents are expected to be identical so that the principal is indifferent ex ante as to who wins the contest, implying that the selection properties of the tournament can be ignored. In this paper we consider a tournament which is not necessarily symmetric, and in which agent type is private information. The principal cares about who wins, but the basic tournament will not achieve perfect selection; the lower-type agent may sometimes win. In a two-player tournament we present a simple reward system in which the winner's reward depends upon which (if any) of two “test standards” is passed; conditions are presented under which this system allows the principal to choose the best agent. This system can be extended in a simple manner to rank types in ann-player tournament. We suggest that the theory can be applied to internal labor markets and research contests.     

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.     

On the complexity of repeated principal agent games?

Summary. We examine an infinitely repeated principal agent game without discounting (Radner [1985] ), in which the agent may engage in multiple projects. We focus on “linear” strategies that summarize each history into a linear function of public outcomes, and select an action according to a single threshold rule. We claim that linear strategies significantly simplify the computation needed to make strategic decisions following each history. Despite the simplicity of linear strategies, we can virtually recover the folk theorem. For any individually rational payoff vector in the interior of the set of feasible expected payoff vectors, there exists a pair of linear strategies that form a Nash equilibrium supporting the target payoff. The equilibrium strategies and the equilibrium payoff vectors form a globally stable solution (Smale [1980] ).     

GRANTING AN EXIT OPTION TO CONDUCT AN AUDIT

We study a principal–agent relationship with auditing in which information from an audit is ‘soft’– by conducting an audit, the principal observes the agent's private information, but cannot obtain verifiable evidence on the information. Moreover, the principal's auditing effort is unverifiable in our model. Therefore, besides the agent's misreporting incentive, there is the principal's incentive to accuse the truthful agent even without auditing. If the principal's auditing effort is verifiable, granting no exit option to the agent is optimal although the principal can still accuse a truthful agent after the audit. We show that when the principal's auditing effort is unverifiable, granting an exit option to the agent and auditing are complementary. Without granting an exit option to the agent, no auditing is optimal, and the principal grants an exit option to conduct a sincere audit, which in turn mitigates the agent's misreporting incentive. Our analysis also reveals that, when the cost of auditing is sufficiently large, the principal conducts more sincere audits with a smaller amount of penalty.     

Garbling of signals and outcome equivalence

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria.Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of ‘being equivalent to’ in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.     

You Don't Always Get What You Pay For: Bonuses,Perceived Income and Effort

Abstract. Consider a principal–agent relationship in which more effort by the agent raises the likelihood of success. This paper provides conditions such that no success bonus induces the agent to exert more effort and the optimal contract is independent of success. Moreover, success bonuses may even reduce effort and thus the probability of success. The reason is that bonuses increase the perceived income of the agent and can hence reduce his willingness to exert effort. This perceived income effect has to be weighed against the incentive effect of the bonus. The tradeoff is determined by the marginal effect of effort on the success probability in relation to this probability itself (success hazard‐rate of effort). The paper also discusses practical implications of the finding.     

Incentives for motivated agents under an administrative constraint

Consider an agent who has an expertise in producing a non-marketable good. This good is valued by a single principal, and there is a verifiable measure of the agent’s performance. Crucially, the agent is intrinsically motivated due to ‘warm glow altruism’. In addition, the agent’s budget, which is controlled by the principal, must not be less than the monetary performance-cost faced by the agent. This gives rise to a limited-liability constraint. It also restricts the agent’s ability to under-report costs. In such environment, we determine the link between the agent’s budget and performance. Our results come in contrast to the received solution of the principal-agent problem and to most in the literature on mission-motivated organisations and public services provision.     

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.     

Present-biased preferences,self-awareness and shirking

We model a mechanism design problem in which the principal owns a project that requires work effort by an agent, but agents may have time-inconsistent, present-biased preferences and lack complete self-awareness of these preferences. The self-control problem and naïveté of an agent may lead him to agree to a contract but later shirk or slack-off, even though doing so is observable. When the principal cannot severely punish shirking and agents are completely naïve, the second-best solution entails allowing a present-biased agent to slack-off in order to avoid a greater loss due to shirking. With greater self-awareness among present-biased agents, the principal may do better by screening some from accepting the contract. Furthermore, when shirking can be severely punished, this does not lead to contracts that eliminate effects of the self control problem. Instead the principal may exploit present-biased agents by offering a contract that allows them to slack-off (which agents fail to foresee they will choose to do) but at the expense of foregoing much compensation.     

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.