Dynamics of multi-player prisoner's dilemma game with coupled players

Abstract

We determine the probability mass distributions of all the possible pair combinations for N = 2, 32 players playing in iterated prisoner's dilemma game setting. In each iteration, player P_n plays with the immediate 2k neighbors only. P_n then probabilistically changes its state in the next play depending on the amount of winning (payoff) received from the previous. Results are different to the standard game (N = 2) as the sensitivity of the players, σ, to their previous payoff is changed.