Influence of conformity on the evolution of cooperation in games with sampling rules on networks

We study the influence of conformity on the evolution of cooperative behavior in games under the learning method of sampling on networks. A strategy update rule based on sampling is introduced into the stag hunt game, where agents draw samples from their neighbors and then update their strategies based on conformity or inference according to the situation in the sample. Based on these assumptions, we present the state transition equations in the dynamic evolution of population cooperation, conduct simulation analysis on lattice networks and scale-free networks, and discuss how this mechanism affects the evolution of cooperation and how cooperation evolves under different levels of conformity in the network. Our simulation results show that blindly imitating the strategies of neighbors does not necessarily lead to rapid consensus in the population. Instead, rational inference through samples can better promote the evolution of the same strategy among all agents in the population. Moreover, the simulation results also show that a smaller sample size cannot reflect the true situation of the neighbors, which has a large randomness, and the size of the benefits obtained in cooperation determines the direction of the entire population towards cooperation or defection. This work incorporates the conforming behavior of agents into the game, uses the method of sampling for strategy updates and enriches the theory of evolutionary games with a more realistic significance.