Characteristic Features of the Sustainable Strategies in the Evolvable Iterated Prisoners’ Dilemma

In the realm of iterated prisoners' dilemma equipped with evolutional generation of strategies, a model has been proposed by Lindgren that allows elongation of genes, represented by onedimensional binary arrays, by three kinds of mutations: duplications, splittings, and point mutations, and the strong strategies are set to survive according to their performance at the change of generations. The actions that the palyers can choose are assumed to be either cooperation represented by C or defection represented by D. It is convenient to 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 in each game. 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 m 2 . We have performed extentive simulations until many long genes appear, 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 determined 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.