Reasoning About Others: Representing and Processing Infinite Belief Hierarchies

In this paper we focus on the problem of how infinite belief hierarchies can be represented and reasoned with in a computationally tractable way. When modeling nested beliefs one usually deals with two types of infinity: infinity of beliefs on every level of reflection and infinity of levels. In this work we assume that beliefs are finite at every level, while the number of levels may still be infinite. We propose a method for reducing the infinite regress of beliefs to a finite structure. We identify the class of infinite belief trees that allow finite representation. We propose a method for deciding on an action based on this presentation. We apply the method to the analysis of auctions. We prove that if the agents’ prior beliefs are not common knowledge, the revenue equivalence theorem ceases to hold. That is, different auctions yield different expected revenue. Our method can be used to design better auction protocols, given the participants’ belief structures.