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We consider N person repeated games with complete information and standard signalling. We first prove several properties of the sets of feasible payoffs and Nash equilibrium payoffs for the n-stage game and for the λ-discounted game. In the second part we determine the set of equilibrium payoffs for the Prisoner's Dilemma corresponding to the critical value of the discount factor.
Sylvain Sorin (Sat,) studied this question.