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.
On the Convergence of Fictitious Play: A Decomposition Approach
29.07.2022
In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence 2022. (pp. pp. 179-185). IJCAI: International Joint Conferences on Artificial Intelligence Organization (2022)
Paper
Elektronische Ressource
Englisch
DDC: | 629 |
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