Opposition of Interest in Subjective Bayesian Theory

A characterization is given of diametrically opposed interests between two players: either neither is a Bayesian, or both have a unique probability and utility function (up to the usual transformation) or both have many possible probabilities and utilities. In the second case, their utility functions must have representations that sum to zero, and they must have identical probability distributions on every uncertain event in the space. Implications of this result for negotiations and for game theory are discussed