Approximate equilibrium in a finitely repeated “Prisoner's dilemma”

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