Evolution of cooperation through aspiration-based adjustment of interaction range in spatial prisoner’s dilemma game

Abstract

Neighborhood size is an important factor in the spatial prisoner’s dilemma game. Traditional static interaction range does not adapt to the dynamic social environment. Therefore, it is necessary to study the adaptive adjustment mechanism of the interaction range. In order to enhance the adaptability of individuals to the dynamic social environment, in this paper we propose an interaction range adjustment mechanism based on the aspiration of payoff. Specifically, the interaction range tends to expand according to a certain probability when the current actual payoff reaches or exceeds the aspired payoff. Otherwise, the interaction range will shrink with a certain probability. Simulation results show that such a mechanism of interaction range adjustment can remarkably promote cooperation. The probability of adjusting the interaction range has a great impact on cooperation evolution. Cooperation can be effectively established in a population in which individuals are with higher shrinkage and lower expansion probabilities. Moreover, the aspiration level is an important factor to affect the effectiveness of the interaction range adjustment. Larger aspiration level is more advantageous to promoting cooperation when the aspiration level is less than 1, while cooperators cannot survive when the aspiration level is larger than 1. The underlying mechanism is furthermore explored, revealing that the ‘isolation zones’ composed of individuals with zero interaction radius play an important role in promoting cooperation.