Evolution of cooperation by reciprocation within structured demes

Abstract

The iterative two-person Prisoners' Dilemma game has been generalised to the N-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT to N-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequency p_c. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invade D. Yet, provided a threshold p_c is crossed, they can coexist stably with D. As N, the size of the group increases, the threshold p_c also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategy D, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.