Analyzing Noisy Observation Game with Bayesian Iterative Conjectures Approach

Abstract

This paper uses Bayesian equilibrium by iterative conjectures approach to solve a noisy sequential game, that is, a sequential game with inaccurate observation clouded by noise. Bayesian equilibrium by iterative conjectures requires players to form conjectures about the strategies of the other players, starting with first order uninformative conjectures and keep updating with game theoretic and statistical decision theoretic reasoning until a convergence of conjectures is achieved. The paper studies an inflationary expectation game where government sets the monetary growth rate which is inaccurately observed by the economic agents. Bayesian iterative conjectures approach generates unique equilibrium which allows insightful and interesting comparative static analysis. The paper also shows that if the statistical decision rule is unspecified in a complete and perfect information sequential game, then there is the issue of indeterminacy in equilibrium solution of such a game. In other words, the current understanding of sequential games as embodied by the solution method of backward induction is just one of the many possible answers. Finally, the paper proves that the Bayesian equilibrium by iterative conjectures approach is a Bayes (undominated) decision rule, attaining the supremum of the expected utility of the player making the inference.