Updating non-additive probabilities - a geometric approach

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non-additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining the notion of independence of non-additive probabilities and Nash equilibrium. Journal of Economic Literature Classification: D81, D83, D84. ∗The first draft of this paper, dated May 1996, was distributed under the title “An Axiomatic Approach to the Conditional Expectation with Non-Additive Probabilities”. †School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel; e-mail: [email protected]; web site: www.math.tau.ac.il/∼lehrer ‡Conversations with David Schmeidler, to whom I am indebted in many respects, were very helpful. My interest in this topic was inspired by Michéle Cohen. I am also grateful to Alain Chateauneuf, Eran Shmaya and Peter P. Wakker for their comments.