Modeling, analysis, and dynamics of Bayesian games via matrix-based method

Abstract

A matrix-based framework for the modeling, analysis and dynamics of Bayesian games are presented using the semi-tensor product of matrices. Static Bayesian games are considered first. A new conversion of Bayesian games is proposed, which is called an action-type conversion. Matrix expressions are obtained for Harsanyi, Selten, and action-type conversions, respectively. Certain properties are obtained, including two kinds of Bayesian Nash equilibria. Then the verification of Bayesian potential games is considered, which is proved to test the solvability of corresponding linear equations equivalently. Finally, the dynamics of evolutionary Bayesian games are considered. Two learning rules for Bayesian potential games are proposed, which are type-based myopic best response adjustment and logit response rule, respectively. Markovian dynamic equations are obtained for the proposed strategy updating rules and convergence is proved.