Strategy evolution of network conformists and rational imitators in the rock–paper–scissors game

The rock–paper–scissors game is a classic example of a three-strategy game in evolutionary game theory, widely employed to study the dynamics of strategy evolution. How to introduce different strategy update rules in the rock–paper–scissors game to study the evolution of strategies is a question worth exploring. In this study, two types of individuals are introduced within a finite and structured population: conformists and rational imitators. Distinct strategy update rules are formulated for each individual type. Conformists update their strategies according to the conformity process, whereas rational imitators update their strategies based on the death–birth process. During the strategy update process, individuals not only adjust their strategies but may also change their types and alter the network structure. Specifically, individuals introduce network dynamics by severing their connection with the neighbor that has the lowest weighted payoff and randomly establishing a new connection with an unconnected individual. This study simulates the aforementioned process on WS small-world and regular networks. The results show that as the proportion of initial rational imitators and the selection intensity increase, the population reaches a stable state more quickly. Over time, the proportion of individuals adopting the same strategy tends to converge across both types. Moreover, we find that the evolutionary outcomes on the WS small-world network are similar to those on the regular network.