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

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 variet...

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Main Author: Sam Ganzfried
Format: Article
Language:English
Published: LibraryPress@UF 2025-05-01
Series:Proceedings of the International Florida Artificial Intelligence Research Society Conference
Subjects:
Online Access:https://journals.flvc.org/FLAIRS/article/view/138636
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author Sam Ganzfried
author_facet Sam Ganzfried
author_sort Sam Ganzfried
collection DOAJ
description 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.
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institution Kabale University
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record_format Article
series Proceedings of the International Florida Artificial Intelligence Research Society Conference
spelling doaj-art-5f22ee14706e4d8e9a49df76851276e12025-08-20T03:49:41ZengLibraryPress@UFProceedings of the International Florida Artificial Intelligence Research Society Conference2334-07542334-07622025-05-0138110.32473/flairs.38.1.138636Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer GamesSam Ganzfried0Ganzfried Research 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. https://journals.flvc.org/FLAIRS/article/view/138636game theoryfictitious playinitializationregret minimizationmultiplayer Nash equilibrium
spellingShingle Sam Ganzfried
Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
Proceedings of the International Florida Artificial Intelligence Research Society Conference
game theory
fictitious play
initialization
regret minimization
multiplayer Nash equilibrium
title Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
title_full Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
title_fullStr Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
title_full_unstemmed Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
title_short Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games
title_sort empirical analysis of fictitious play for nash equilibrium computation in multiplayer games
topic game theory
fictitious play
initialization
regret minimization
multiplayer Nash equilibrium
url https://journals.flvc.org/FLAIRS/article/view/138636
work_keys_str_mv AT samganzfried empiricalanalysisoffictitiousplayfornashequilibriumcomputationinmultiplayergames