The Folk Theorem for repeated games suggests that finding Nash equilibria in repeated games should be easier than in one-shot games. In contrast, we show that the problem of finding any Nash equilibrium for a three-player infinitely-repeated game is as hard as it is in two-player one-shot games....

We provide an algorithm for testing the substitutability of a length-N preference relation over a set of contracts X in time O(|X|3⋅N3). Access to the preference relation is essential for this result: We show that a substitutability-testing algorithm with access only to an agentʼs choice...

of cooperating and defecting agents at equilibrium.