Correlated equilibria in two-player repeated games with nonobservable actions

Four kinds of correlated equilibrium payoff sets in undiscounted repeated games with nonobservable actions are studied. Three of them, the upper, the uniform, and Banach lead to the same payoff set, whereas the lower one in general is associated with a larger set. The extensive form correlated equilibrium is also explored. It turns out that both the regular and extensive form correlated equilibria yield the same sets of payoffs.