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.

翻译：多智能体随机博弈中，仅有少数几类博弈能保证独立学习收敛至纳什均衡。马尔可夫潜在博弈正是这类博弈的关键范例。既有研究已归纳出判定随机博弈为马尔可夫潜在博弈的若干充分条件，然而这些条件往往对博弈结构施加严格限制且难以验证。为突破上述局限，Mguni等人[12]提出了马尔可夫潜在博弈的松弛定义，并给出另一组将随机博弈归类为潜在博弈的必要条件。基于该条件，作者声称可通过求解对偶马尔可夫决策过程高效计算确定性纳什均衡。本文通过构造反例，提供了反驳上述论断的证据。