Evolution of Grim Trigger in Prisoner Dilemma Game with Partial Imitation
The emergence of Grim Trigger as the dominant strategy in the Iterated Prisoner Dilemma (IPD) on a square lattice is investigated for players with finite memory, using three different kinds of imitation rule: the traditional imitation rule where the entire data base of the opponent’s moves is copied, and the two more realistic partial imitation rules that copy only a subset of opponent’s moves based on information of games played. We find that the dominance of Grim Trigger is enhanced at the expense of some well known strategies such as tit-for-tat (TFT) when a player has access only to those moves observed in past games played with his opponents. The evolution of the clusters of Grim Trigger in the early stage of the games obeys a common pattern for all imitation rules, before these clusters of Grim Triggers coalesce into larger patches in the square lattice. A physical explanation for this pattern evolution is given. Implication of the partial imitation rule for IPD on complex networks is discussed.
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