Calculation of Perfect Bayesian Equilibrium in a Signaling Game

In the teaching of dynamic games with incomplete information, the solution of perfect Bayesian equilibrium is a difficult point. Although there is no general solution to the general dynamic games with incomplete information, there is a general solution method to the signaling games. Most of the existing game theory textbooks do not give clear solving methods and specific calculation steps. This paper analyses how to calculate the perfect Bayesian equilibrium of an extensive-form signaling game through an example. In this paper, Gibbons' definition of perfect Bayesian equilibrium is taken as the definition of perfect Bayesian equilibrium. The definition attaches four requirements to Nash equilibrium. That is, in a dynamic game with incomplete information, the Nash equilibrium satisfying these four requirements is a perfect Bayesian equilibrium. The calculation process is divided into 4 steps. First, the belief hypothesis. Second, analysis of the signal receiver’s strategy and the requirements for the posterior probability. Third, analysis of the signal sender’s behavior according to different belief combinations. Finally, the posterior probabilities are analyzed using the requirements 3 and 4 in the perfect Bayesian equilibrium definition. On the basis of the previous analyses, the perfect Bayesian equilibria of the signaling game can be calculated step by step.