Markov games with coupling constraints provide a natural framework to study constrained decision-making involving self-interested agents, where the feasibility of an individual agent's strategy depends on the joint strategies of the others. Such games arise in numerous real-world applications involving safety requirements and budget caps, for example, in environmental management, electricity markets, and transportation systems. While correlated equilibria have emerged as an important solution concept in unconstrained settings due to their computational tractability and amenability to learning, their constrained counterparts remain less explored. In this paper, we study constrained correlated equilibria-feasible policies where any unilateral modifications are either unprofitable or infeasible. We first characterize the constrained correlated equilibrium showing that different sets of modifications result in an equivalent notion, a result which may enable efficient learning algorithms. We then address existence conditions. In particular, we show that a strong Slater-type condition is necessary in games with playerwise coupling constraints, but can be significantly weakened when all players share common coupling constraints. Under this relaxed condition, we prove the existence of a constrained correlated equilibrium.

翻译：具有耦合约束的马尔可夫博弈为研究涉及自利智能体的约束决策问题提供了一个自然框架，其中单个智能体策略的可行性取决于其他智能体的联合策略。此类博弈广泛存在于涉及安全要求和预算上限的现实应用中，例如环境管理、电力市场和交通系统。尽管相关均衡因其计算可处理性和易于学习的特性，已成为无约束场景下的重要解概念，但其约束版本的研究仍相对不足。本文研究约束相关均衡——即任何单方面修改均无利可图或不可行的可行策略。我们首先刻画约束相关均衡的特征，证明不同的修改集合会导致等价的概念，这一结果可能为高效学习算法的设计提供基础。随后我们探讨存在性条件：特别地，我们证明在具有玩家间耦合约束的博弈中，强Slater型条件是必要的；但当所有玩家共享共同耦合约束时，该条件可显著弱化。在此松弛条件下，我们证明了约束相关均衡的存在性。