Don't Bet on It
If two people have diﬀerent probability assessments about the realization of an uncertain event, they can design a contingent agreement such as a bet or gamble that oﬀers each of them positive expected value. Yet, in the process of formulating this kind of agreement, information about the basis for each person’s probabilities may be indirectly revealed to the other. The very willingness to accept a proposed bet conveys information. This paper models a process by which private, asymmetrically-held information is progressively unveiled as a possible contingent agreement is discussed. If the two parties share priors and their information partitions are common knowledge, simple discussion of the acceptability of any proposed bet is shown to reveal enough about their private information to render the bet unacceptable.
Geanakoplos, John and Sebenius, James K., "Don't Bet on It" (1982). Cowles Foundation Discussion Papers. 876.