Pure strategy equilibria in finite symmetric concave games and an application to symmetric discrete Cournot games. (English) Zbl 1417.91129
von Mouche, Pierre (ed.) et al., Equilibrium theory for Cournot oligopolies and related games. Essays in honour of Koji Okuguchi. Cham: Springer. Springer Ser. Game Theory, 89-100 (2016).
Summary: 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.
For the entire collection see [Zbl 1338.91012].
For the entire collection see [Zbl 1338.91012].
MSC:
| 91A40 | Other game-theoretic models |
| 91B54 | Special types of economic markets (including Cournot, Bertrand) |
| 91A80 | Applications of game theory |
Keywords:
payoff function; strategy profile; real interval; inverse demand function; pure strategy equilibriumReferences:
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