Effect of spatial structure on the evolution of cooperation based on game models

To elucidate the mechanisms for the evolution of cooperation has been a core problem in biology, economics and sociology. Evolutionary game theory has proven to be an efficient approach to investigate the problem by using models based on so-called social dilemmas. Spatial structure is indicated to have an important effect on the evolution of cooperation and has been intensively studied during recent years. From this perspective, we review our studies in evolutionary dynamics based on a repeated game with three strategies, 'always defect' (ALLD), 'tit-for-tat' (TFT), and 'always cooperate' (ALLC). With mathematical analysis and numerical simulations, the results show that cooperation can be promoted in spatially-structured populations. Cooperators prevail against defectors by forming stable clusters, which is called the `spatial selection'. Meanwhile, lattice structure also inhibits cooperation due to the advantage of being spiteful. Furthermore, simulations demonstrate that a slight enforcement of ALLC can only promote cooperation when there is weak network reciprocity, while the catalyst effect of TFT on cooperation is verified