Evolutionary dynamics of cooperation in dynamic networked systems with active striving mechanism

Abstract

How the cooperation between individuals emerges in complex networked systems is a hot issue of common concern in many different fields. Evolutionary game theory has provided a mathematical framework for studying this problem. In social networks, the interaction between individuals is not fixed, but constantly changing. Therefore, this paper considers the coevolution of strategy and network structure when studying the evolutionary dynamics of cooperation. For the linking dynamics, different from the traditional random selection of connection objects, we propose a mechanism that individuals can actively recommend themselves before being selected. Through such active efforts, individuals expect to get more opportunities to be connected. In particular, the attributes of individuals considered in this paper have two characteristics without correlation. One is strategy, that is, cooperation or defection, and they have their own intensities of self recommendation respectively. The other is the high or low response to others’ recommendation, which reflects whether individuals are easy to be persuaded. We make a theoretical analysis of the system under the limit condition that the linking dynamics are much faster than strategy evolution. It is found that when the self recommendation intensity of the defector is greater than that of the cooperator, it is not conducive to the emergence of cooperation. On the contrary, when cooperators make self recommendation more actively than defectors, the response levels of different types of individuals and their proportion in the system jointly determine whether cooperation emerges. We theoretically analyze the conditions that can promote cooperation when the recommendation intensity of cooperators is high. However, the arms race in which both sides actively strive to raise the intensity of self recommendation will lead to an increasing adjustment cycle and form a Red Queen like evolution.