2024/05/13 by Fatemeh Fardno, Fardno, Fatemeh, Seyed Majid Zahedi +1
Decision Sciences · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Applications #Multiagent Systems (cs.MA)
paper · pdf · doi:10.48550/arxiv.2405.08206
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of sufficient conditions for a stochastic game to qualify as a Markov potential game. However, these conditions often impose strict limitations on the game's structure and tend to be challenging to verify. To address these limitations, Mguni et al. [12] introduce a relaxed notion of Markov potential games and offer an alternative set of necessary conditions for categorizing stochastic games as potential games. Under these conditions, the authors claim that a deterministic Nash equilibrium can be computed efficiently by solving a dual Markov decision process. In this paper, we offer evidence refuting this claim by presenting a counterexample.