Coexistence of competing strategies in evolutionary games

Many investigations have been carried out in order to get an idea of what the driving forces behind cooperative behaviors of selfish individuals are. A wide variety conflicts between individual and collective interests are ubiquitous in social life, especially in those situations associated with collective actions based on joint decisions made by the group. Cooperation is widespread but hard to understand from the viewpoint of Darwinian’s selection. Individual heterogeneity is one of the most often observed phenomena in realistic systems. There are several ways how this feature can be built into a model, and this subject is still in urgent need of research. Henceforth our thesis mainly concerns about the individual heterogeneity referring to strategies, time scales and transferring probabilities as follows. First, we propose a novel approach to investigate the strategy updating in the framework of evolutionary games, based on player’s switching probabilities between two competing players. Results suggest that it is an effective analysis tool in studying why and how different strategies coexist in large populations. Then we focus our attention on the multiple options of individuals in the decision making, and study the competition results among them. Results help to illustrate the basic mechanism how cooperation gets supported when players face multiple choices. Finally, we break the traditional frame of homogeneous time scales for strategy updating among populations, and introduce individual difference in terms of times scales. Our main conclusion is that the heterogeneity in time scales of individuals’ updates will drastically enrich evolutionary dynamics.