Abstract
We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner's dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.
Highlights
One major challenge in fields ranging from genetics and cell biology to evolutionary anthropology and behavioral economics is the emergence and persistence of cooperation [1,2]
Resulting is a social dilemma, which typically leads to widespread defection
We focus on prisoner’s dilemma game (PD) games by limiting 0ƒDgƒ1, 0ƒDrƒ1 and r = Dg~Dr, where r is the costto-benefit ratio [61]
Summary
One major challenge in fields ranging from genetics and cell biology to evolutionary anthropology and behavioral economics is the emergence and persistence of cooperation [1,2]. Two players simultaneously decide to adopt one of strategies: cooperation (C) or defection (D). If both cooperate (defect) they receive the reward R (the punishment P). One player chooses cooperation while the other defects, the latter gets the temptation T and the former is left with the sucker’s payoff S These payoffs satisfy the ranking T.R.P.S and 2R.T+S; defection optimizes the individual payoff, in spite of the fact that mutual cooperation could yield a higher collective benefit. Resulting is a social dilemma, which typically leads to widespread defection. To overcome this unfortunate outcome, special scenarios that support the evolution of cooperation need to be suggested
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