The number of strategy changes can be used to promote cooperation in spatial snowdrift game

In evolutionary games, the optimal strategy is derived from repeated trial and error. The strategy that has been maintained in the recent period is more likely a desirable choice. This paper proposes a mechanism for the snowdrift game on a square lattice and tries to facilitate cooperation. The new mechanism encourages individuals to choose a strategy that can meet a given aspiration level for a long time. The core of this mechanism lies in two aspects: (i) If an individual randomly selects a neighbour and obtains a return that does not meet the aspiration level, he will directly switch strategy without referring to strategies of others. (ii) When the aspiration level is met, we take the number of strategy changes in the past few rounds of every individual as a parameter, and an individual learns its selected neighbour’s strategy by Fermi updating rule in case of his number of strategy changes is not smaller than his selected neighbour’s. The simulation results show that the low aspiration level is conductive to the emergence of cooperative behaviour and that the novel mechanism significantly improves the level of cooperation. It is worth mentioning that the cooperation level always remains at 1 for the (1-aspiration level) part of the cost-to-benefit ratio r.