Memory-limited Strategies in Iterated Prisoner's Dilemma
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Game theory studies the optimal strategy when a player's fate is determined by both of the player's and its opponent's moves. Basically, each player is not free from other players' existence and should strongly interact with them to succeed. The Prisoner's Dilemma game, one of the most famous game-theoretic models, has been extensively studied to explain how rational individuals do or do not achieve cooperation. In its iterated version, there appear some nice cooperating strategies such as Tit-for-tat, Grim Trigger, and Pavlov, each of which refers to only the last step to decide its move. However, it is not known if they work well among the more intelligent strategies which remember the last two steps, where the strategy space to be explored becomes much larger than the previous case. Here we show that this larger horizon can be searched effectively by combining the results from replicator dynamics, and that this space allows the rise of a modified version of Tit-for-tat, which remedies the vulnerability to error between Tit-for-tat's. This modified Tit-for-tat is expected to be highly robust whenever the error occurs with a sufficiently low probability. This observation implies the role of memory in evolution as a refined kin detector to repair an error.