Baudin, L and Laraki, R 
ORCID: 0000-0002-4898-2424
(2022)
Fictitious Play and Best-Response Dynamics in Identical Interest and Zero Sum Stochastic Games.
In: ICML, 2022-7-17 - 2022-7-23, Baltimore, Maryland USA.
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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).
| Item Type: | Conference or Workshop Item (Unspecified) |
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| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 15 Aug 2022 07:41 |
| Last Modified: | 14 Jul 2023 22:08 |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3161090 |
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