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

Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games