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Representing equilibrium aggregates in aggregate games with applications to common agency

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  • Martimort, David
  • Stole, Lars
Abstract
An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.

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  • Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, vol. 76(2), pages 753-772.
    • Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:753-772
    DOI: 10.1016/j.geb.2012.08.005
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    Cited by:

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    4. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    5. Martimort, David & Semenov, Aggey & Stole, Lars A., 2018. "A complete characterization of equilibria in an intrinsic common agency screening game," Theoretical Economics, Econometric Society, vol. 13(3), September.
    6. Toomas Hinnosaar, 2019. "Price Setting on a Network," Papers 1904.06757, arXiv.org.
    7. Evangelos Toumasatos & Stein Ivar Steinshamn, 2018. "Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre- and Post-Brexit Context," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-48, June.
    8. Jin Yeub Kim & Yongjun Kim & Myungkyu Shim, 2023. "Do Financial Analysts Herd?," Global Economic Review, Taylor & Francis Journals, vol. 52(3), pages 202-219, July.
    9. Heid, Benedikt & Stähler, Frank, 2024. "Structural gravity and the gains from trade under imperfect competition: Quantifying the effects of the European Single Market," Economic Modelling, Elsevier, vol. 131(C).
    10. Hefti, Andreas, 2017. "Equilibria in symmetric games: theory and applications," Theoretical Economics, Econometric Society, vol. 12(3), September.
    11. Martimort, David & Semenov, Aggey & Stole, Lars, 2015. "A Complete Characterization of Equilibria in Two-type Common Agency Screening Games," MPRA Paper 66620, University Library of Munich, Germany.
    12. Martimort, David & Stole, Lars, 2024. "Menu Auctions Under Asymmetric Information," TSE Working Papers 24-1592, Toulouse School of Economics (TSE).
    13. Kim Jin Yeub & Shim Myungkyu, 2019. "Forecast Dispersion in Finite-Player Forecasting Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(1), pages 1-6, January.
    14. David Martimort & Aggey Semenov & Lars Stole, 2016. "A Complete Characterization of Equilibria in Common Agency Screening Games," Working Papers 1618E, University of Ottawa, Department of Economics.
    15. Perrin Lefebvre & David Martimort, 2023. "Reform for Sale : A Common Agency Model with Moral Hazard Frictions," Post-Print hal-04234620, HAL.
    16. Toumasatos, Evangelos & Steinshamn, Stein Ivar, 2017. "Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre and Post Brexit Context," Discussion Papers 2017/11, Norwegian School of Economics, Department of Business and Management Science.
    17. Robertas Zubrickas, 2020. "Contingent wage subsidy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(4), pages 1105-1119, August.
    18. Martimort, David & Stole, Lars, 2015. "Menu Auctions and Influence Games with Private Information," MPRA Paper 62388, University Library of Munich, Germany.
    19. Simon P. Anderson & Nisvan Erkal & Daniel Piccinin, 2020. "Aggregative games and oligopoly theory: short‐run and long‐run analysis," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 470-495, June.
    20. Zubrickas, Robertas, 2014. "The provision point mechanism with refund bonuses," Journal of Public Economics, Elsevier, vol. 120(C), pages 231-234.
    21. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.

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    More about this item

    Keywords

    Aggregate games; Common agency games; Supply-function games;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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