Pure Strategy Equilibria in Finite Symmetric Concave Games and an Application to Symmetric Discrete Cournot Games
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.
- Cheng SF, Reeves DM, Vorobeychik Y, Wellman MP (2004) Notes on equilibria in symmetric games. In: Proceedings of the 6th international workshop on game theoretic and decision theoretic agents, New YorkGoogle Scholar
- Favati P, Tardella F (1990) Convexity in nonlinear integer programming. Ric Oper 53:3–44Google Scholar
- Moulin H (1986) Game theory for the social sciences. NYU Press, New YorkGoogle Scholar