In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are two-player non-zero-sum with 3 pure strategies per player. Shapley assumed that each player played a specific pure strategy in the first round. We show that if we use random (mixed) strategy profile initializations we are able to converge to Nash equilibrium approximately 1/3 of the time for a representative game in this class.

翻译：1964年, Shapley设计了一套游戏, 虚剧无法与纳什均衡相融合。 这些游戏是2人非零和,每个玩家有3个纯策略。 Shapley假设每个玩家在第一轮中都玩了一个特定的纯策略。 我们显示,如果我们使用随机( 混合) 战略配置初始化, 我们就可以在这个班级有代表性游戏的时间里 大约三分之一的时间 与纳什平衡相融合 。