Markov \alpha-Potential Games
We propose a new framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games to study Markov games. We show that any Markov game with finite-state and finite-action is a Markov <inline-formula><tex-math...
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| Vydáno v: | IEEE transactions on automatic control s. 1 - 16 |
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2025
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | We propose a new framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games to study Markov games. We show that any Markov game with finite-state and finite-action is a Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential game, and establish the existence of an associated <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential function. Any optimizer of an <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential function is shown to be an <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-stationary Nash equilibrium. We study two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, via the framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games, with explicit characterization of an upper bound for <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula> and its relation to game parameters. Additionally, we provide a semi-infinite linear programming based formulation to obtain an upper bound for <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula> for any Markov game. Furthermore, we study two equilibrium approximation algorithms, namely the projected gradient-ascent algorithm and the sequential maximum improvement algorithm, along with their Nash regret analysis, and corroborate the results with numerical experiments. |
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| AbstractList | We propose a new framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games to study Markov games. We show that any Markov game with finite-state and finite-action is a Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential game, and establish the existence of an associated <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential function. Any optimizer of an <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential function is shown to be an <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-stationary Nash equilibrium. We study two important classes of practically significant Markov games, Markov congestion games and the perturbed Markov team games, via the framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games, with explicit characterization of an upper bound for <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula> and its relation to game parameters. Additionally, we provide a semi-infinite linear programming based formulation to obtain an upper bound for <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula> for any Markov game. Furthermore, we study two equilibrium approximation algorithms, namely the projected gradient-ascent algorithm and the sequential maximum improvement algorithm, along with their Nash regret analysis, and corroborate the results with numerical experiments. |
| Author | Guo, Xin Wu, Manxi Li, Xinyu Maheshwari, Chinmay Sastry, Shankar |
| Author_xml | – sequence: 1 givenname: Xin surname: Guo fullname: Guo, Xin email: xinguo@berkeley.edu organization: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA, USA – sequence: 2 givenname: Xinyu surname: Li fullname: Li, Xinyu email: xinyu_li@berkeley.edu organization: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA, USA – sequence: 3 givenname: Chinmay surname: Maheshwari fullname: Maheshwari, Chinmay email: chinmay_maheshwari@jhu.edu organization: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA – sequence: 4 givenname: Shankar surname: Sastry fullname: Sastry, Shankar email: sastry@eecs.berkeley.edu organization: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, USA – sequence: 5 givenname: Manxi surname: Wu fullname: Wu, Manxi email: manxiwu@berkeley.edu organization: Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, CA, USA |
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| Snippet | We propose a new framework of Markov <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula>-potential games to study Markov games. We... |
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| SubjectTerms | Approximation algorithms Equilibrium approximation algorithms Games Heuristic algorithms Linear programming Markov games Markov potential games Measurement Multi-agent reinforcement learning Nash equilibrium Postal services Regret analysis Topology Training Upper bound |
| Title | Markov \alpha-Potential Games |
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