Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
This provides incremental improvements for researchers and practitioners in game theory by addressing convergence issues in non-zero-sum and multiplayer games.
The paper tackled the problem of Nash equilibrium computation in multiplayer games, showing that fictitious play leads to improved approximation over regret minimization and can solve challenge problems with random initializations, achieving positive results despite negative theoretical guarantees.
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.