Parameterization of equilibrium assessment in Bayesian game with its application to belief computation

In this paper, the authors show that for a certain kind of Bayesian games, there exists parametric representation in terms of an equilibrium assessment, a pair of a Bayesian Nash equilibrium and a corresponding belief. The parameterization can be derived from a steady-state analysis of a deterministic state-space model that transfers from the equilibrium assessment to one. The resulting parameterization is expressed in fractional form and its ratio is unchanged by transitions of the equilibrium assessment. Owing to the constant ratio, the parameterization enables belief computation using a given or measured BNE as a game outcome. A numerical example confirms the validity and usefulness of the parameterization.

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