that cost and demand functions are not sufficient for a general theory of oligopoly, and the economists must include the context within which oligopolies operate in their theory. In 2007, Borgs et al. proved that, despite the folk theorem, in the general case computing the Nash equilibria for repeated games is not easier than computing the Nash equilibria for one-shot finite games, a problem which lies in the PPAD complexity class. The practical consequence of this is that no efficient (polynomial-time) algorithm is known that computes the strategies required by folk theorems in the general case. Summary of folk theorems The following table compares various folk theorems in several aspects: Horizon – whether the stage game is repeated finitely or infinitely many times. Utilities – how the utility of a player in the repeated game is determined from the player's utilities in the stage game iterations. Conditions on G (the stage game) – whether there are any technical conditions that should hold in the one-shot game in order for the theorem to work. Conditions on x'' (the target payoff vector of the repeated game) – whether the theorem works for any individually rational and feasible payoff vector, or only on a subset of these vectors. Equilibrium type – if all conditions are met, what kind of equilibrium is guaranteed by the theorem – Nash or Subgame-perfect? Punishment type – what kind of punishment strategy is used to deter players from deviating? Notes References A set of introductory notes to the Folk Theorem. Game theory equilibrium concepts Theorems