Evolutionary Game Gynamics Driven by Heterogeneous Self-learning Rules

How to achieve full cooperation among large numbers of individuals is essential for both artificial and biological systems. Learning rules (or updating rules), which specify how individuals change their behavior over time, are vital to probe this problem. Here, we incorporate individual heterogeneity into the self-evaluation process and propose the heterogeneous self-learning dynamics. When the selection intensity is weak, we analytically derive that the final outcomes of the heterogeneous dynamics can be obtained by combining the outcomes of all the corresponding homogeneous dynamics in well-mixed populations. Meanwhile, a simple condition is found which tells whether one behavior will be more abundant than the other in the long run. All of our analytical results are verified by simulations. Our work thus reveals some interesting characteristics of heterogeneous self-learning dynamics.