论文标题
在最佳响应动力学下的收敛游戏的频率
The Frequency of Convergent Games under Best-Response Dynamics
论文作者
论文摘要
随机生成普通形式游戏的回报矩阵，我们在$ n $ - 玩家的合奏中使用独特的纯策略NASH平衡来计算游戏的频率。这些是完全可预测的，因为它们必须融合到NASH平衡。然后，我们考虑在最佳响应动态下汇聚一类更广泛的游戏，每个玩家都依次选择了最佳的纯策略。我们表明，随着玩家的数量或策略数量流向无穷大，收敛游戏的频率变为零。在$ 2 $ - 玩家的情况下，我们表明，对于具有至少$ 10 $策略的大型游戏，具有多种纯策略NASH Equilibria的收敛游戏比具有独特的NASH平衡的游戏更有可能。我们的小说方法使用$ n $ - 分段图来描述游戏。
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games goes to zero as the number of players or the number of strategies goes to infinity. In the $2$-player case, we show that for large games with at least $10$ strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an $n$-partite graph to describe games.
