Approximate Equilibrium in a Finitely Repeated Prisoner’s Dilemma

The paper studies a finitely repeated Prisoner’s Dilemma. To maintain cooperation in the game, a new profile of behavior strategies is proposed, where the deviation of a player is punished not until the end of the game, but rather for a given number of stages depending on the stage of the game. The existence of an approximate equilibrium or epsilon-equilibrium in these strategies is proven, and the maximum payoff of a player deviating from the approximate equilibrium is found.