The truth behind the myth of the folk theorem

We study the problem of computing an ε-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players as polynomial-time Turing machines that maintain state (rather than stateless polynomial-time Turing machines)---and make some standard cryptographic hardness assumptions (the existence of public key encryption), the problem can actually be solved in polynomial time.