he gains in the short run, and this gain can be wiped out only if the punishment gives the deviator strictly less utility than the agreement path. The following folk theorems are known for the overtaking criterion: Strict stationary equilibria: A Nash equilibrium is called strict if each player strictly prefers the infinite sequence of outcomes attained in equilibrium, over any other sequence he can deviate to. A Nash equilibrium is called stationary if the outcome is the same in each time-period. An outcome is attainable in strict-stationary-equilibrium if-and-only-if for every player the outcome is strictly better than the player's minimax outcome. Strict stationary subgame-perfect equilibria: An outcome is attainable in strict-stationary-subgame-perfect-equilibrium, if for every player the outcome is strictly better than the player's minimax outcome (note that this is not an "if-and-only-if" result). To achieve subgame-perfect equilibrium with the overtaking criterion, it is required to punish not only the player that deviates from the agreement path, but also every player that does not cooperate in punishing the deviant. The "stationary equilibrium" concept can be generalized to a "periodic equilibrium", in which a finite number of outcomes is repeated periodically, and the payoff in a period is the arithmetic mean of the payoffs in the outcomes. That mean payoff should be strictly above the minimax payoff. Strict stationary coalition equilibria''': With the overtaking criterion, if an outcome is attainable in coalition-Nash-equilibrium, then it is Pareto efficient and weakly-coalition-individually-rational. On the other hand, if it is Pareto efficient and strongly-coalition-individually-rational it can be attained in strict-stationary-coalition-equilibrium. Infinitely-repeated games with discounting Assume that the payoff of a player in an infinitely repeated game is given by the average discounted criterion with discount factor 0 < δ < 1: The discount factor indicates how patient the players are. The factor is introduced so that the payoff remain bounded when . The folk theorem in this case requires that the payoff profile in the repeated game strictly dominates the minmax payoff profile (i.e., each player receives strictly more than the minmax payoff). Let a be a strategy profile of the stage game with payoff profile u which strictly dominates the minmax payoff profile. One can define a Nash equilibrium of the game with u as resulting payoff profile as follows: 1. All players start by playing a and continue to play a if no deviation occurs. 2. If any one player, say player i,