Emergence of an unpredictable evolution in a spatial prisoner’s dilemma via a player’s multiple perspectives

Spatial prisoner’s dilemma (SPD) has attracted researchers’ attention as a model of conflict for players. In SPD, players have two different strategies, namely, defectors and cooperators. A defector earns a high payoff from an opponent co-operator while getting nothing from an opponent defector. On the contrary, cooperators promote a win–win relationship between the two cooperators. These mechanisms influence population dynamics in SPD, and many SPD models have been developed. However, little is known about the emergence of an unstable or unpredictable evolution in population dynamics using an SPD model, which may be observed in living systems. In addressing this issue, two SPD models were proposed. In both models, players change the neighborhood definition in accordance with their strategies and sometimes select the rule for this change using probability or local information. Result showed that our models generated characteristic population patterns that may be linked to a self-organized criticality (SOC), a term referring to many systems of interconnected, nonlinear elements that evolve over time into a critical state. In fact, the second model could be spontaneously close to the critical point using local information.