Pure strategy equilibria in finite symmetric concave games and an application to symmetric discrete Cournot games
Pure strategy equilibria in finite symmetric concave games and an application to symmetric discrete Cournot games
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有限对称凹博弈中的纯策略均衡及其在对称离散古诺博弈中的应用
DOI：
10.1007/978-3-319-29254-0_7
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Takuya Iimura and Takahiro Watanabe
中科院分区：
文献类型：
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作者：
Takuya Iimura;Pierre von Mouche and Takahiro Watanabe;Takuya Iimura and Takahiro Watanabe
我们考虑一个有限对称博弈，其中每个参与人的策略集合是一个一维整数区间。我们证明了当支付函数相对于自己的策略是凹的并且满足对称策略轮廓附近的一对对称条件时，存在一个纯策略均衡。作为应用，我们考虑一个对称古诺博弈，其中每个企业选择一个整数数量的产品。结果表明，如果行业收益函数为凹函数，需求逆函数为不增加函数，成本函数为凸函数，则企业的收益函数满足条件，且该对称博弈具有纯策略均衡。
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.