While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact leads to improved Nash equilibrium approximation over a variety of game classes and sizes than (counterfactual) regret minimization, which has recently produced superhuman play for multiplayer poker. We also show that when fictitious play is run several times using random initializations it is able to solve several known challenge problems in which the standard version is known to not converge, including Shapley's classic counterexample. These provide some of the first positive results for fictitious play in these settings, despite the fact that worst-case theoretical results are negative.

翻译：尽管虚构博弈在特定博弈类别（如双人零和博弈）中保证收敛至纳什均衡，但在非零和博弈与多玩家博弈中并不保证收敛。我们证明，相较于（反事实）遗憾最小化算法——该算法近期在多玩家扑克博弈中实现了超越人类的表现，虚构博弈实际上能在多种博弈类别与规模下实现更优的纳什均衡逼近。我们还发现，当采用随机初始策略多次运行虚构博弈时，该算法能够解决若干已知的挑战性问题（包括沙普利经典反例），而标准版本在这些问题中已知无法收敛。尽管最坏情况下的理论结果是否定的，这些发现为虚构博弈在此类场景中的应用提供了首批积极证据。