Evolution of cooperation in heterogeneously stochastic interactions

Abstract

• We propose a novel game model with heterogeneously stochastic interactions. • Our model shows that heterogeneously stochastic interactions promote cooperation. • The probability distribution meets the power-law, exponential and uniform distributions. Heterogeneity is omnipresent in the real world, which plays a vital role in affecting the evolution of cooperation. Within this paper, we will discard the hypothesis of deterministic interactions among individuals and further propose a novel game model with heterogeneously stochastic interactions to mainly investigate the evolution of cooperation on a 2D square lattice, in which individuals play games with their neighbors in accordance with the probability of different heterogeneous distributions, such as power-law, exponential and uniform distribution, respectively. Through abundant numerical simulations, we find that such a simple setup has different effects on the evolution of cooperation in different social dilemmas. For the prisoner’s dilemma game and snowdrift game, the evolution of cooperation can be significantly facilitated. While for the stag hunt game, heterogeneously stochastic interactions can even impede the evolution of cooperation. Thus, we mainly focus on the impact of heterogeneously stochastic interaction on the evolution of cooperation under the prisoner’s dilemma and snowdrift game. On the whole, the stronger heterogeneity in the interaction probability can bring more benefit to the evolution of cooperation. We also verify the robustness of the proposed model with other potential structures and strategy update pattern, and the results are almost qualitatively consistent. Our exploration further clarifies the positive role of heterogeneity in the evolution of cooperation, which can help us to deeply comprehend the persistence or emergence of collective cooperation occurring on top of many natural and social systems.