collusionjuly2010 - Unravelling in a Repeated Moral Hazard...

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Unformatted text preview: Unravelling in a Repeated Moral Hazard Model with Multiple Agents * Madhav Chandrasekher † Current Draft: July 16, 2010 Abstract : Consider an infinite horizon repeated moral hazard problem where a single principal employs several agents. The principal cannot observe the agent’s effort choices; however, agents can observe each other and can be contractually required to make obser- vation reports to the principal. This paper addresses the existence of an approximately efficient contract for this environment. We construct a class of contracts with the following two properties. First, payoffs to agents in any pure strategy equilibrium of the induced game are bounded above by the first-best, perfect information benchmark as the discount factor gets large (i.e. the contract is collusion-proof). Second, there is an efficient equilib- rium in which this bound is attained in the limit. Keywords : Repeated Games, Collusion, Communication, Statistical Testing. * Acknowledgments: I would like to thank Bob Anderson, Sambuddha Ghosh, Natalia Kovri- jnykh, Alejandro Manelli, Daniel Monte, Yuliy Sannikov, Ed Schlee, Chris Shannon, and especially Hector Chade for comments and suggestions. Any errors are my own. † Mailing address: Department of Economics, W.P. Carey School of Business, P.O. Box 873806, Tempe, AZ 85287-3806; E-mail address: [email protected] 1 Introduction This paper studies a contract design problem when a principal hires several agents over an infinite time horizon. Effort is unobservable to the principal, but agents can observe each other. We add a communication phase to the standard (single agent) model, so that between the time when effort is taken and output is realized, each agent can be required to make a publicly verifiable report of his observations of his co-workers’ effort choices. As in the single agent model, wages in any period are contingent only on the principal’s information, i.e. the history of output data and observation reports. To place the infinite horizon problem in context, first consider the static multiple- agent contract problem. Variations of this contracting environment have been stud- ied in a series of papers, e.g. Holmstrom (1982), Mookherjee (1984), Ma (1988), Ma et al. (1988), Miller (1997) among others. The model closest to ours is the one in Ma (1988). Ma proposes the following solution to the optimal contract problem. The contract has two components, insurance and a stochastic bonus (reward). Each player is assigned a monitor and is, in turn, assigned to be some other player’s mon- itor. Moreover, between the time when effort is chosen and output is realized each monitor is called upon to issue a report on the effort choice of the player he monitors....
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This note was uploaded on 04/28/2011 for the course BUS 315 taught by Professor Powell during the Spring '11 term at University of Hawaii, Manoa.

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collusionjuly2010 - Unravelling in a Repeated Moral Hazard...

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