We exploit the properties of homogeneous functions to characterize the symmetric pure-strategy Nash equilibria of n-player symmetric games in which each player’s revenue function is not homogeneous but it can be decomposed into the sum of homogeneous functions with different degrees of homogeneity. Our results aim to provide a pathway for an easy computation of symmetric equilibria for this type of games. We discuss our results in a Cournot game, a contest game, and a public good game.

中文翻译：

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利用具有非同质收入函数的游戏的同质性

我们利用齐次函数的性质来表征n人对称博弈的对称纯策略纳什均衡，其中每个玩家的收益函数不是齐次的，但可以分解为不同同质程度的齐次函数之和。我们的结果旨在为此类博弈的对称均衡的轻松计算提供一条途径。我们在古诺博弈、竞赛博弈和公益博弈中讨论我们的结果。