On the Convergence of Fictitious Play: A Decomposition Approach

Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in \(n\)-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable convergence guarantees on zero-sum games and potential games...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Chen, Yurong, Deng, Xiaotie, Li, Chenchen, Mguni, David, Wang, Jun, Yan, Xiang, Yang, Yaodong
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Decomposition
Game theory
Games
Machine learning
Multiagent systems
Zero sum games
Online Access:Get full text
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Summary:Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in \(n\)-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable convergence guarantees on zero-sum games and potential games, many real-world problems are often a mixture of both and the convergence property of FP has not been fully studied yet. In this paper, we extend the convergence results of FP to the combinations of such games and beyond. Specifically, we derive new conditions for FP to converge by leveraging game decomposition techniques. We further develop a linear relationship unifying cooperation and competition in the sense that these two classes of games are mutually transferable. Finally, we analyze a non-convergent example of FP, the Shapley game, and develop sufficient conditions for FP to converge.
ISSN:2331-8422