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Selecting equilibria in common agency games


  • Martimort, David
  • Stole, Lars


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.

Suggested Citation

  • Martimort, David & Stole, Lars, 2009. "Selecting equilibria in common agency games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 604-634, March.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:604-634

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    References listed on IDEAS

    1. Laussel, Didier & Le Breton, Michel, 2001. "Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency," Journal of Economic Theory, Elsevier, vol. 100(1), pages 93-128, September.
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    3. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    4. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    5. David Martimort & Lars Stole, 2009. "Market participation in delegated and intrinsic common-agency games," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 78-102.
    6. Laussel, Didier & Le Breton, Michel, 1998. "Efficient Private Production of Public Goods under Common Agency," Games and Economic Behavior, Elsevier, vol. 25(2), pages 194-218, November.
    7. Chiesa, Gabriella & Denicolò, Vincenzo, 2009. "Trading with a common agent under complete information: A characterization of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 144(1), pages 296-311, January.
    8. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, March.
    9. Kirchsteiger, Georg & Prat, Andrea, 2001. "Inefficient equilibria in lobbying," Journal of Public Economics, Elsevier, vol. 82(3), pages 349-375, December.
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    Cited by:

    1. Lastauskas, Povilas, 2013. "Europe's revolving doors: Import competition and endogenous firm entry institutions," Kiel Advanced Studies Working Papers 464, Kiel Institute for the World Economy (IfW).
    2. Semenov, Aggey, 2010. "Common agency with risk-averse agent," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 38-49, January.
    3. Graham Mallard, 2014. "Static Common Agency And Political Influence: An Evaluative Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 17-35, February.
    4. Matteo Bassi & Marco Pagnozzi & Salvatore Piccolo, 2015. "Product Differentiation by Competing Vertical Hierarchies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(4), pages 904-933, October.
    5. Christos Bilanakos, 2011. "Optimal Contracts and Investment in General Human Capital under Common Agency," University of Cyprus Working Papers in Economics 08-2011, University of Cyprus Department of Economics.
    6. Martimort, David & Semenov, Aggey, 2008. "Ideological uncertainty and lobbying competition," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 456-481, April.
    7. Rohan Dutta & David K Levine & Salvatore Modica, 2017. "Damned if You Do and Damned if You Don't: Two Masters," Levine's Working Paper Archive 786969000000001420, David K. Levine.
    8. Piccolo, Salvatore & D'Amato, Marcello & Martina, Riccardo, 2008. "Product market competition and organizational slack under profit-target contracts," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1389-1406, November.


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