Fictitious Play and Best-Response Dynamics in Identical Interest and Zero-Sum Stochastic Games
Abstract
This paper proposes an extension of a popular decentralized discrete-time learning procedure when repeating a static game called fictitious play (FP) (Brown, 1951; Robinson, 1951) to a dynamic model called discounted stochastic game (Shapley, 1953). Our family of discrete-time FP procedures is proven to converge to the set of stationary Nash equilibria in identical interest discounted stochastic games. This extends similar convergence results for static games (Monderer & Shapley, 1996a). We then analyze the continuous-time counterpart of our FP procedures, which include as a particular case the best-response dynamic introduced and studied by Leslie et al. (2020) in the context of zero-sum stochastic games. We prove the converge of this dynamics to stationary Nash equilibria in identical-interest and zero-sum discounted stochastic games. Thanks to stochastic approximations, we can infer from the continuous-time convergence some discrete time results such as the convergence to stationary equilibria in zero-sum and team stochastic games (Holler, 2020).
BibTeX
@InProceedings{pmlr-v162-baudin22a,
title = {Fictitious Play and Best-Response Dynamics in Identical Interest and Zero-Sum Stochastic Games},
author = {Baudin, Lucas and Laraki, Rida},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {1664--1690},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/baudin22a/baudin22a.pdf},
url = {https://proceedings.mlr.press/v162/baudin22a.html},
abstract = {This paper proposes an extension of a popular decentralized discrete-time learning procedure when repeating a static game called fictitious play (FP) (Brown, 1951; Robinson, 1951) to a dynamic model called discounted stochastic game (Shapley, 1953). Our family of discrete-time FP procedures is proven to converge to the set of stationary Nash equilibria in identical interest discounted stochastic games. This extends similar convergence results for static games (Monderer & Shapley, 1996a). We then analyze the continuous-time counterpart of our FP procedures, which include as a particular case the best-response dynamic introduced and studied by Leslie et al. (2020) in the context of zero-sum stochastic games. We prove the converge of this dynamics to stationary Nash equilibria in identical-interest and zero-sum discounted stochastic games. Thanks to stochastic approximations, we can infer from the continuous-time convergence some discrete time results such as the convergence to stationary equilibria in zero-sum and team stochastic games (Holler, 2020).}
}