I consider a moral hazard problem with risk neutral parties, limited liability, and an informed principal. The contractible outcome is correlated to both the principal's private information and the agent's hidden action. In contrast to a model without a privately informed principal or without limited liability, I show that the first-best payoff cannot be implemented by any equilibrium mechanism. Furthermore, limited liability precludes the existence of equilibrium refinements such as (Strongly) Neologism proofness. * I am grateful to Eddie Dekel, Asher Wolinsky, and Bruno Strulovici for their invaluable comments.
We consider a sequential search environment in which the searching agent does not observe the quality of goods. The agent can contract with a profit-maximizing principal who sells a signal about a good's quality but cannot commit to future contracts. The agent is willing to pay a high price for a more informative signal today, but an agent who anticipates high prices in the future is less likely to continue searching due to a low continuation value, thereby reducing the principal's future profits. We show that there is an essentially unique stationary equilibrium in which the principal (i) induces the socially efficient stopping rule, (ii) fully extracts the surplus generated from search, and (iii) persuades the agent against settling for marginal quality goods, thus extending the duration of rent extraction. Our results demonstrate that the principal would not gain from long-term commitment power or considering complicated, non-stationary contracts.
I study a continuous time principal-agent model in which an unknown parameter and the agent's hidden effort affect the distribution of observable outcomes. The principal and the agent learn about the parameter by observing past outcomes. The agent's current effort has an implicit long-term effect through the belief dynamics and a deviation in effort creates a persistent disparity between the principal's and the agent's beliefs. This disparity affects the rate of learning as well as how the two evaluate the expected distribution of future outcomes which in turn affects their evaluation of future payoffs. Placing minimal restrictions on how effort and the parameter interact, I derive necessary and sufficient conditions for incentive compatible contracts. In addition to the agent's promised utility, the covariance between the on-path posterior beliefs and the agent's total payoff serves as a second state variable capturing the marginal long-run effects of effort.
We study how changes to the informativeness of signals in Bayesian games and single‐agent decision problems affect the distribution of equilibrium actions. Focusing on supermodular environments, we provide conditions under which a more precise private signal for one agent leads to an increasing‐mean spread or a decreasing‐mean spread of equilibrium actions for all agents. We apply our comparative statics to information disclosure games between a sender and many receivers and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information.
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