The No Trade Principle and the Characterization of Compact Beliefs
Ngai-Ching Wong
Department of Applied Mathematics
National Sun Yat-sen University
wong@math.nsysu.edu.tw
We establish the no trade principle, i.e., the no trade theorem and its converse, for any dual pair of bet and extended belief spaces, defined on a given measurable space. A key condition is that, except perhaps one of the agents, everyone else has (weak*) compact sets of beliefs. We find out that in most of the models of uncertainty adopted in the economic literature, roughly speaking, the epistemic statement that an agent has a compact set of beliefs is equivalent to the economic statement that he has an open cone of positive bets. This improves our understanding of what compactness actually means within an economic context.