This paper introduces constrained correlated equilibrium, a solution concept combining correlation and coupled constraints in finite non-cooperative games. In the general case of an arbitrary correlation device and coupled constraints in the extended game, we study the conditions for equilibrium. In the particular case of constraints induced by a feasible set of probability distributions over action profiles, we first show that canonical correlation devices are sufficient to characterize the set of constrained correlated equilibrium distributions and provide conditions of their existence. Second, it is shown that constrained correlated equilibria of the mixed extension of the game do not lead to additional equilibrium distributions. Third, we show that the constrained correlated equilibrium distributions may not belong to the polytope of correlated equilibrium distributions. Finally, we illustrate these results through numerical examples.

翻译：本文提出了一种结合有限非合作博弈中关联性与耦合约束的解概念——受限关联均衡。针对扩展博弈中任意关联装置与耦合约束的一般情形，我们研究了均衡的存在条件。在行动概型概率分布可行集诱导约束的特殊情形下：首先证明标准关联装置足以刻画受限关联均衡分布集的特征，并给出其存在性条件；其次表明博弈混合扩展中的受限关联均衡不会产生新的均衡分布；第三，揭示受限关联均衡分布可能不属于关联均衡分布的多面体；最后通过数值算例验证上述结论。