Analysis of payoff expectation in evolutionary game based on Bush–Mosteller model

In both human society and natural systems, clustered groups often exhibit “experience” or “learning” effects. Thus, individuals’ decisions are often influenced based on their past experiences. However, the social dilemma of fostering and sustaining cooperation through “experience” or “learning” effects in the decision-making process of behavioral evolution has been largely overlooked. Scholars primarily focus on the evolution of behavioral decision-making through changes in decision-making processes and associated benefits. Despite existing research showing the difficulty for individuals to achieve cooperation through “experience” or “learning” effects. This paper aims to simplify and enhance the behavioral decision-making evolution model based on prior research. Building on previous research, the Bush–Mosteller (BM) model will be utilized to analyze the behavior of individual agents in evolutionary games by assigning benefit expectations within the model. The results indicate that profit expectation A, as defined in the BM model, can effectively foster cooperative behavior among individuals within a specific numerical range with the introduction of altruism u. Additionally, this highlights the direct impact of the threshold of expectation A on enhancing cooperative behavior.