Agreement and stochastic independence of belief functions

Abstract

In this paper, we look at a strategic situation in which each player may lack perfect understanding of the opponents' information structures, and as a result, his beliefs about the opponents' action choices are represented by a belief function (totally monotone capacity). If players' beliefs are common knowledge, then they agree, but do not necessarily take any form that can be interpreted as stochastic independence. An extra condition that ensures stochastic independence is identified. The results clarify the foundation and motivate variants of an existing generalized Nash equilibrium concept.