Effects of directional migration for pursuit of profitable circumstances in evolutionary games

Abstract

Migration has been verified to promote the evolution of cooperation in evolutionary games. Two factors determine the impacts of migration on cooperation, the migration speed and the migration direction of individuals. In previous works, migration direction is determined either in a random way or by referring to some rational factors, such as moving closer to cooperators and escaping away from defectors. However, in order to pursue profitable circumstances, individuals might decide their migration direction based on the neighbors’ trends instead of their positions. In this work, we propose two models by introducing two different directional migrations respectively into evolutionary games in a continuous two-dimensional plane. In one model, individuals adopt the average migration directions of their cooperative neighbors, which is called the cooperator-following (CF) migration model. In the other one, the defector-leaving (DL) migration model, individuals move in the opposite directions to their defective neighbors. Our results show that, for both models, the appropriate migration speeds can significantly promote cooperation and there exist optimal speeds to maximize the cooperation level in the population. Moreover, we find that the CF model is superior to the DL model in improving cooperation in most parameter regions. Besides, we simulate the models with different interaction radiuses and different population densities, and find that the optimization of cooperation by the migration speed still exist.