Equilibrium Selection under the Bayes-Based Strategy Updating Rules

In this paper, first, an evolutionary game model for Bayes-based strategy updating rules was constructed, in which players can only observe a signal that reveals a strategy type instead of the strategy type directly, which deviates from the strategy type of players. Then, the equilibrium selection of populations in the case of the asymmetric game, the Battle of the Sexes (BoS), and the case of a symmetric coordination game was studied where individuals make decisions based on the signals released by each player. Finally, it was concluded that in the BoS game, when the accuracy of the signal is low, the population eventually reaches an incompatible state. If the accuracy of the signal is improved, the population finally reaches a coordinated state. In a coordination game, when the accuracy of the signal is low, the population will eventually choose a payoff-dominated equilibrium. With the improvement of signal accuracy, the equilibrium of the final selection of the population depends on its initial state.