  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.
