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Equilibrium convergence in large games

Author

Listed:
  • Chen, Enxian
  • Wu, Bin
  • Xu, Hanping

Abstract

This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of finite-player games, the limit of any convergent sequence of Nash equilibria of the corresponding finite-player games can be induced by a Nash equilibrium of the large game. Such a result goes beyond earlier results on the closed graph property for pure strategy Nash equilibrium correspondence in large games in multiple aspects. An application on equilibrium selection in large games is also presented.

Suggested Citation

  • Chen, Enxian & Wu, Bin & Xu, Hanping, 2025. "Equilibrium convergence in large games," Journal of Mathematical Economics, Elsevier, vol. 117(C).
    • Handle: RePEc:eee:mateco:v:117:y:2025:i:c:s030440682500014x
    DOI: 10.1016/j.jmateco.2025.103097
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    More about this item

    Keywords

    Large games; Finite-player games; Nash equilibrium; Closed graph property;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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