Finding a prototype form of sustainable strategies for the iterated prisoners dilemma

Abstract

We deal with a multi-agent model of the iterated prisoners' dilemma with evolvable strategies, originally proposed by Lindgren that allows elongation of genes represented by one-dimensional binary arrays, by means of three kinds of mutations: the duplication, the fission, and the point mutation, and the strong strategies are set to survive according to their performance at every generation change. The actions that the players can choose are assumed to be either cooperation (represented by C) or defection (represented by D). We conveniently use 0,1 instead of D,C. Each player has a strategy that determines the player's action based on the history of actions chosen by both players. Corresponding to the history of actions, represented by a binary tree of depth m, a strategy is represented by the leaves of that tree, an one-dimensional array of length 2m. We have performed extentive simulations until many long genes are generated by mutations, and by evaluating those genes we have discovered that the genes of high scores are constructed by 3 common quartet elements, [1001], [0001], and [0101]. Furthermore, we have found that the strong genes commonly have the element [1001 0001 0001 0001] that have the following four features: 1 never defects under the cooperative situation, represented by having '1' in the fourth element of the quartet such as [***1], 2 retaliates immediately if defected, represented by having '0' in the first element and the third element in the quartet such as [0*0*], 3 volunteers a cooperative action after repeated defections, represented by '1' in the first element of the genes, 4 exploits the benefit whenever possible, represented by having '0' in the quartet such as [*0**]. This result is stronger and more specific compared to [1**1 0*** 0****001] reported in the work of Lindgren as the structure of strong genes. © 2013 Springer-Verlag Berlin Heidelberg.