*2.2. Evolutionary Game Theory*

Evolutionary game theory is different from the assumption of the completely rational man in traditional game theory, which holds that man is a bounded rationality. The research object of game theory is multiple market participants, and it discusses the dynamic evolution of system groups. In evolutionary game theory, the participating groups have an active learning ability, can constantly choose and try to make mistakes through mutual imitation and learning, and can constantly change the basic behavior strategies of the game players, so as to maximize their own benefits. Smith proposed that the basis of constructing the evolutionary game model was mutation and choice [56]. Mutation refers to the solution to diversity stability in evolutionary games. Choice refers to the process of making choices by learning or imitating in groups and constantly optimizing one's own choices, that is, the process of generating higher payments [57]. According to the mutation and choice theory in evolutionary game theory, replication dynamic equation and evolutionary stability strategy constitute the core of the evolutionary game model. Copying the dynamic equation is actually a dynamic strategy adjustment mechanism. It is assumed that the game players (insiders) are all bounded, rational people, and the individuals in the group with a lower income than the average will change their strategies and learn from the surrounding group members whose income is higher than their own. Therefore, the probability of each strategy choice of the game players in the group will change accordingly. Evolutionary Stable Strategy (ESS), as another core concept in evolutionary game theory, reflects the stable state of the equilibrium solution of the system. Evolutionary stability strategy thinks that the optimal equilibrium of people's game is a function to be revised, so evolutionary stability strategy cannot be achieved at the beginning. It can only be achieved through trial and error and learning, and through the repetition of games by players to modify and improve individual strategies. Among the current research, Fan et al. developed an evolutionary game model to analyze the operation mechanism of local governments' different expenditure preferences regarding the production behavior of industrial polluting enterprises [58]; Liu et al. applied an evolutionary game model to analyze the necessity and effect of orderliness–synergy in the sustainable development of China's power generation industry during the transition period [59]; Su investigated the evolutionary decisionmaking process and stable strategies of three stakeholders involved in the construction waste recycling industry based on the evolutionary game model [60]. However, no scholar has thus far employed the evolutionary game model to analyze the behavioral strategies of stakeholders involved in energy-saving renovations of existing rural residential buildings. In this work, we construct a tripartite evolutionary game model to analyze the evolutionary rules and stable strategies of tripartite behaviors regarding energy-saving renovations of existing rural residential buildings, and analyze the influencing factors accordingly.
