Sayın, Muhammed ÖmerZhang, KaiqingOzdaglar, Asuman2023-02-262023-02-262022-07-12978145039150-4http://hdl.handle.net/11693/111763Conference Name: 23rd ACM Conference on Economics and Computation, EC 2022Date of Conference: 11-15 July 2022Certain but important classes of strategic-form games, including zero-sum and identical-interest games, have thefictitious-play-property (FPP), i.e., beliefs formed in fictitious play dynamics always converge to a Nash equilibrium (NE) in the repeated play of these games. Such convergence results are seen as a (behavioral) justification for the game-theoretical equilibrium analysis. Markov games (MGs), also known as stochastic games, generalize the repeated play of strategic-form games to dynamic multi-state settings with Markovian state transitions. In particular, MGs are standard models for multi-agent reinforcement learning - a reviving research area in learning and games, and their game-theoretical equilibrium analyses have also been conducted extensively. However, whether certain classes of MGs have the FPP or not (i.e., whether there is a behavioral justification for equilibrium analysis or not) remains largely elusive. In this paper, we study a new variant of fictitious play dynamics for MGs and show its convergence to an NE in n-player identical-interest MGs in which a single player controls the state transitions. Such games are of interest in communications, control, and economics applications. Our result together with the recent results in [42] establishes the FPP of two-player zero-sum MGs and n-player identical-interest MGs with a single controller (standing at two different ends of the MG spectrum from fully competitive to fully cooperative). © 2022 Owner/Author.EnglishFictitious playIdentical-interest gamesMarkov gamesZero-sum gamesConference Paper10.1145/3490486.3538289