Constrained Correlated Equilibria

This paper studies constrained correlated equilibrium, a solution concept combining correlation and coupled constraints in finite non-cooperative games. In a correlated equilibrium, players coordinate their actions based on common random signals, yielding outcomes that can be more efficient than Nash equilibria but may lack feasibility when considering certain constraints. We present the formal definition of the concept, illustrating its relevance through examples. Furthermore, we analyze its fundamental properties, including relations to correlated equilibria. In the particular case of constraints induced by a feasible set of probability distributions over action profiles, we show that canonical correlation devices suffice to characterize the set of constrained correlated equilibrium distributions and provide a sufficient condition of the existence of the constrained correlated equilibrium. Finally, we illustrate these results through numerical examples.