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Sequential common agency

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In a common agency game a set of principals promises monetary transfers to an agent which depend on the action he will take. The agent then chooses the action, and is paid the corresponding transfers. Principals announce their transfers simultaneously. This game has many equilibria; Bernheim and Whinston ([1]) prove that the action chosen in the coalition-proof equilibrium is e±cient. The coalition-proof equilibria have an alternative characterization as truthful equilibria. The other equilibria may be ine±- cient. Here we study the sequential formulation of the common agency game: principals announce their transfers sequentially. We prove that the set of equilibria is di®erent in many important ways. The outcome is e±cient in all the equilibria. The truthful equilibria still exist, but are no longer coalition-proof. Focal equilibria are now a di®erent type of equilibria, that we call thrifty. In thrifty equilibria of the sequential games, principals are better o® (and the agent worse o®) than in the truthful equilibria of the simultaneous common agency. These results suggest that the sequential game is more desirable institution, because it does not have ine±cient equilibrium outcomes; but it is less likely to emerge when agents have the power to design the institution.

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