Sviatoslav Brainov and Tuomas Sandholm
In this paper we convert the auction game to a Bayesian decision problem with an infinite hierarchy of beliefs. We propose a solution to a such Bayesian decision problem. The solution is a generalization of the solution of Tan and Werlang (1988) and can be applied to finite as well as to infinite belief trees. The solution coincides with the standard Bayesian solution for finite trees and for trees representing common knowledge.