Cooperative behaviors in spatial multi-game based on Hawkes processes

Abstract

As for collective behaviors in reality, the occurrence of similar events in group is not independent, in which the occurrence historical events, such as frequencies, interval time, etc, would have an incentive effect on their recurrence probability. In spired by this, Hawkes process is first introduced into evolutionary game model. Different from the existing works, the game behaviors in a networked group change from certainty to probabilistic behaviors affected by historical events. Specifically, an incentive effect will occur with the occurrence of game behaviors as well as decay with the lapse of time. Based on the above probabilistic game mechanism, a multi-game model is proposed, where players are assumed to be emotional for their owned resources. In general, the results of game behaviors would determine the allocation of resources, and the owned quantities of resources would affect the emotion of players. As a feedback loop, it finally affects the game strategy of players. In experiments, the mutual effect of limited resources and game strategy based on probabilistic game mechanism is quantitatively studied. Meanwhile, a phase transition of cooperative behaviors is explored, which is mainly arising from the probabilistic game processes and the evolving emotions of players.