Is Evolutionary Game Nash Equilibrium?

Evolutionary game theory is a theory that combines game theory analysis with dynamic evolution process analysis. Methodologically, it is different from game theory, which focuses on static equilibrium and relative static equilibrium and emphasizes a dynamic equilibrium. Evolutionary game theory originated from the theory of biological evolution and successfully explained some phenomena in the process of biological evolution. Nowadays, economists use evolutionary game theory to analyze social habits, norms, systems or their influencing factors and explain their formation process, and have achieved remarkable results. Evolutionary game theory has become an important analytical tool of evolutionary economics and has gradually developed into a new field of economics. ……

In traditional game theory, participants are completely rational. Usually, under the assumption of complete rationality, if Nash equilibrium exists, then both sides of the game can directly reach Nash equilibrium once. This result does not depend on the initial state of the market, so it does not need any dynamic adjustment process.

Evolutionary game theory holds that Nash equilibrium can only be achieved after many games and needs a dynamic adjustment process. Balance depends on the initial state and path.

In addition, in the case of multiple Nash equilibria, if a Nash equilibrium must be adopted, then there must be some mechanism that can lead to a certain equilibrium expected by each participant. The concept of Nash equilibrium in game theory itself does not have this mechanism.

Therefore, when there are multiple Nash equilibria in the game, even assuming that all participants are completely rational, it is impossible to predict the outcome of the game. If players only have limited rationality, it is more difficult to predict the outcome of the game.

Of course, in game theory, when there are multiple Nash equilibria, the Nash equilibria can be refined by backward induction, but the prerequisite of this method is that participants need to meet a rational assumption stronger than complete rationality-sequential rationality. This cannot be achieved in reality.

In evolutionary game theory, the refinement of equilibrium is achieved by positive induction, that is, participants choose their future behavior strategies according to the history of the game, which is a dynamic selection and adjustment process. Therefore, although the participants are bounded and rational, the dynamic selection mechanism will make one of them reach a Nash equilibrium when there are multiple Nash equilibria, and realize the refinement of Nash equilibrium. ..... for reference.