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Large Aggregate Games with Heterogeneous Players

Author

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  • Serrano-Padial, Ricardo

    (School of Economics)

Abstract

We study large games played by heterogeneous agents whose payoffs depend on the aggregate action and provide novel equilibrium selection and comparative statics results. Regarding equilibrium selection, we establish the equivalence between potential maximization and the global games selection in supermodular games, and characterize the uniquely selected equilibrium as the strategy profile that maximizes the ex-ante expected payoffs of a player with marginal beliefs. To obtain our equivalence result we show that (i) payoffs in an aggregative potential game must be quasilinear and (ii) beliefs in the global game must satisfy a generalized Laplacian property linking (weighted) average beliefs to the uniform distribution. We present comparative statics results that rely on average rather than pointwise conditions on payoffs and use them to illustrate how heterogeneity affects equilibrium levels of the aggregate action.

Suggested Citation

  • Serrano-Padial, Ricardo, 2021. "Large Aggregate Games with Heterogeneous Players," School of Economics Working Paper Series 2021-2, LeBow College of Business, Drexel University, revised 06 Dec 2021.
    • Handle: RePEc:ris:drxlwp:2021_002
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    More about this item

    Keywords

    aggregative games; potential games; global games; comparative statics; noise-independent selection; Laplacian beliefs;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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