Selecting Equilibria in Common Agency Games

Posted: 16 Feb 2014

See all articles by Lars Stole

Lars Stole

University of Chicago - Booth School of Business

David Martimort

Paris School of Economics (PSE)

Date Written: October 20, 2007


We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices. As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information.

Keywords: Common agency, Complete information, Asymmetric information, Common screening device, Equilibrium selection, Public good

JEL Classification: D82

Suggested Citation

Stole, Lars A. and Martimort, David, Selecting Equilibria in Common Agency Games (October 20, 2007). Journal of Economic Theory, Vol. 144, 2009. Available at SSRN:

Lars A. Stole (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7309 (Phone)
773-702-0458 (Fax)

David Martimort

Paris School of Economics (PSE) ( email )

48 Boulevard Jourdan
Paris, 75014 75014

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