Mutual Cooperation Due to TFT Strategy Observing Fixed Number of Cooperative Players

Reputation theories that give a solution to 2-persons Prisoner Dilemma have a common assumption that all players observe what happened in all other players. However, the assumption that a player has to observe all others seems to be unrealistic. To overcome this problem, Nakai and Muto (2008) proposed us-Tit For Tat (TFT) strategy that requires a player to regard another player who did not cooperate with himself/herself and his/her “friends” as a friend, and they showed emergence of a mutually cooperative society. They assume that the us-TFT player doesn’t have to observe all other players and observe him/herself and his/her friends. However, when all players become mutual friends, they observe all other players, and hence us-TFT suffers from the same weakness of previous studies. To solve this, we propose a new us-TFT strategy with which a player observes a small fixed number of other players. The players to be observed are selected based on how cooperative they are toward the us-TFT player. We performed evolutionary simulations with ALL_D, ALL_C, the us-TFT etc and foundemergence of a mutual cooperative society. Especially, in case that the number to be observed is two, mutual cooperation is the most likely to emerge. Therefore, it is concluded that mutual cooperation can emerge without observing all others and it is a new finding. In addition, we examined what mechanism works. The takeoff begins when a player changes into an ALL_C player by an accident. After that, there appear friendships between the ALL_C players and us-TFT players. The ALL_C player is positioned at center of the network, and us-TFT players surround the ALL_C player. Therefore, the network looks a star-like one and grows into a mutually friendly network.