In reality, the dependency relationship among individuals is heterogeneous and time-varying. Based on this fact, we present a new mechanism of coevolution of game strategy and link weight when analyzing the evolution of cooperation. In detail, we model the population on a regular network, on which the relationship between players is depicted by a weighted link, and prisoner's dilemma has been applied to describe the interaction of players. Further, the impact of this mechanism on the cooperative behavior has been outlined. By conducting large-scale Monte Carlo simulations, we can easily draw a conclusion that this mechanism can promote cooperation efficiently. Compared with the traditional case, when the temptation of defection b is large, the fraction of cooperation is still able to keep in a high level. With a comprehensive examination of the distribution of stable link weight, it is evident that the coevolution mechanism would deviate the initial distribution. This mechanism induces the heterogeneity of players, which enhances the fraction of cooperation. Numerical simulations also indicate that an intermediate value of Δ/δ warrants an optimal resolution of prisoner's dilemma. The mechanism of coevolution of game strategy and link weight has a practical significance and will provide new insight for the further research. It's generally acknowledged that networks are helpful in describing complex systems. Likewise, the interactions among people are often modeled within the network theoretical framework. Particularly interesting in this context is the time-varying nature of human interdependencies that qualitatively corresponds to the change of link weights in a network. Accordingly, we augment the standard mechanism of evolutionary game theory, whereby individuals adopt the game strategy of their more successful peers, with the simultaneous evolution of link weights. We thus examine the emergence of cooperative behavior as a result of the coevolution of game strategy and link weight. How cooperative behavior evolved is still an open scientific question, generating humongous interest among scholars from multiple disciplines [1] [2] [3] [4] [5] . To address such an overarching question, the pioneering works in the field resorted to the framework of evolutionary game theory [6] [7] [8] . Prisoner's dilemma 9,10 and public goods game 11-14 served as the paradigms for expressing a social dilemma in the cases of pairwise and group interactions, respectively. In these two types of games, defection always represents the optimal choice irrespective of the opponent's decision. Yet, if defection is the preferred option, how did cooperation prevail in the real world? Following a number of attempts to resolve the conundrum of cooperation, Nowak in 2006 reviewed five rules for the promotion of cooperation named kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection 15 . Subsequently, the effects of a number of complementary mechanisms were also examined, including reward 11, 13, 16 , punishment [17] [18] [19] , and reputation [20] [21] [22] , to name a few. In parallel to the mechanisms that promote cooperation, the results of Nowak and May from 1992 sparked interest in the role of the spatial structure in the evolution of cooperative behavior 23 . Studies that followed placed evolutionary games into networks with small-world [24] [25] [26] , scale-free [27] [28] [29] , and a number of other topologies [30] [31] [32] [33] [34] [35] . More recently, coevolutionary scenarios 36 emerged as a promising way of improving the odds for the evolution of cooperation, whereby strategies and some
Huang et al. REF present a new model for the coevolution of game strategy and link weight.
Understanding Cooperative Behavior Based on the Coevolution of Game Strategy and Link Weight
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Scientific reports
Computer Science Medicine