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Pure Strategy Equilibria in Finite Symmetric Concave Games and an Application to Symmetric Discrete Cournot Games

In: Equilibrium Theory for Cournot Oligopolies and Related Games

Author

Listed:
  • Takuya Iimura
  • Takahiro Watanabe

    (Tokyo Metropolitan University)

Abstract

We consider a finite symmetric game where the set of strategies for each player is a one-dimensional integer interval. We show that a pure strategy equilibrium exists if the payoff function is concave with respect to the own strategy and satisfies a pair of symmetrical conditions near the symmetric strategy profiles. As an application, we consider a symmetric Cournot game in which each firm chooses an integer quantity of product. It is shown, among other things, that if the industry revenue function is concave, the inverse demand function is nonincreasing, and the cost function is convex, then the payoff function of the firm satisfies the conditions and this symmetric game has a pure strategy equilibrium.

Suggested Citation

  • Takuya Iimura & Takahiro Watanabe, 2016. "Pure Strategy Equilibria in Finite Symmetric Concave Games and an Application to Symmetric Discrete Cournot Games," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 89-100, Springer.
    • Handle: RePEc:spr:spschp:978-3-319-29254-0_7
    DOI: 10.1007/978-3-319-29254-0_7
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