Abstract: The existence of many biological systems,
especially human societies, is based on cooperative behavior
[1, 2]. If natural selection favors selfish individuals, then what
mechanism is at work that we see so many cooperative
behaviors? One answer is the effect of network structure. On a
graph, cooperators can evolve by forming network bunches
[2, 3, 4]. In a research, Ohtsuki et al used the idea of iterated
prisoners- dilemma on a graph to model an evolutionary
game. They showed that the average number of neighbors
plays an important role in determining whether cooperation is
the ESS of the system or not [3]. In this paper, we are going to
study the dynamics of evolution of cooperation in a social
network. We show that during evolution, the ratio of
cooperators among individuals with fewer neighbors to
cooperators among other individuals is greater than unity. The
extent to which the fitness function depends on the payoff of
the game determines this ratio.