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Unraveling in a Repeated Moral Hazard Model with Multiple Agents ∗
, 2013
"... Abstract: This paper studies an infinite horizon repeated moral hazard problem where a single principal employs several agents. We assume that the principal cannot observe the agents ’ effort choices; however, agents can observe each other and can be contractually required to make observation report ..."
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Abstract: This paper studies an infinite horizon repeated moral hazard problem where a single principal employs several agents. We assume that the principal cannot observe the agents ’ effort choices; however, agents can observe each other and can be contractually required to make observation reports to the principal. Observation reports, if truthful, can serve as a monitoring instrument to discipline the agents. However, reports are cheap talk so that it is also possible for agents to collude, i.e. where they shirk, earn rents, and report otherwise to the principal. The main result of the paper constructs a class of collusionproof contracts with two properties. First, equilibrium payoffs to both the principal and the agents approach their firstbest benchmarks as the discount factor tends to unity. These payoff bounds apply to all subgame perfect equilibria in the game induced by the contract. Second, while equilibria themselves depend on the discount factor, the contract which induces these equilibria is independent of the discount factor.
Monomial strategies for concurrent reachability games and other stochastic games?
"... Abstract. We consider twoplayer zerosum finite (but infinitehorizon) stochastic games with limiting average payoffs. We define a family of stationary strategies for Player I parameterized by ε> 0 to be monomial, if for each state k and each action j of Player I in state k except possibly one ..."
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Abstract. We consider twoplayer zerosum finite (but infinitehorizon) stochastic games with limiting average payoffs. We define a family of stationary strategies for Player I parameterized by ε> 0 to be monomial, if for each state k and each action j of Player I in state k except possibly one action, we have that the probability of playing j in k is given by an expression of the form cεd for some nonnegative real number c and some nonnegative integer d. We show that for all games, there is a monomial family of stationary strategies that are εoptimal among stationary strategies. A corollary is that all concurrent reachability games have a monomial family of εoptimal strategies. This generalizes a classical result of de Alfaro, Henzinger and Kupferman who showed that this is the case for concurrent reachability games where all states have value 0 or 1. 1