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      Fictitious play in Markov games with single controller

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      Author(s)
      Sayın, Muhammed Ömer
      Zhang, Kaiqing
      Ozdaglar, Asuman
      Date
      2022-07-12
      Source Title
      Proceedings of the 23rd ACM Conference on Economics and Computation
      Publisher
      Association for Computing Machinery, Inc
      Pages
      919 - 936
      Language
      English
      Type
      Conference Paper
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      Abstract
      Certain 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.
      Keywords
      Fictitious play
      Identical-interest games
      Markov games
      Zero-sum games
      Permalink
      http://hdl.handle.net/11693/111763
      Published Version (Please cite this version)
      https://dx.doi.org/10.1145/3490486.3538289
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