Effects of non-uniform number of actions by Hawkes process on spatial cooperation

Abstract

The emergence of cooperative behavior, despite natural selection favoring rational self-interest, presents a significant evolutionary puzzle. Evolutionary game theory elucidates why cooperative behavior can be advantageous for survival. However, the impact of non-uniformity in the frequency of actions, particularly when actions are altered in the short term, has received little scholarly attention. To demonstrate the relationship between the non-uniformity in the frequency of actions and the evolution of cooperation, we conducted multi-agent simulations of evolutionary games. In our model, each agent performs actions in a chain-reaction, resulting in a non-uniform distribution of the number of actions. To achieve a variety of non-uniform action frequency, we introduced two types of chain-reaction rules: one where an agent's actions trigger subsequent actions, and another where an agent's actions depend on the actions of others. Our results revealed that cooperation evolves more effectively in scenarios with even slight non-uniformity in action frequency compared to completely uniform cases. In addition, scenarios where agents' actions are primarily triggered by their own previous actions more effectively support cooperation, whereas those triggered by others' actions are less effective. This implies that a few highly active individuals contribute positively to cooperation, while the tendency to follow others' actions can hinder it.