随机初始化可解决Shapley的虚拟博弈反例问题
Random Initialization Solves Shapley's Fictitious Play Counterexample
AI总结：
针对Shapley1964年提出的虚拟博弈无法收敛的双人非零和博弈反例，研究发现采用随机混合策略初始化，可使该类代表性博弈以约1/3的概率收敛到纳什均衡。
摘要：
1964年，Shapley设计了一类博弈，在这类博弈中虚拟博弈无法收敛到纳什均衡。这类博弈为双人非零和博弈，每名参与者有3种纯策略。Shapley假设每名参与者在首轮都采用特定的纯策略。我们证明，若使用随机（混合）策略剖面初始化，对于该类别中的一个代表性博弈，我们能以约1/3的概率收敛到纳什均衡。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
