  In a prediction market, individuals can sequentially place bets on the
outcome of a future event. This leaves a trail of personal probabilities for
the event, each being conditional on the current individual's private
background knowledge and on the previously announced probabilities of other
individuals, which give partial information about their private knowledge. By
means of theory and examples, we revisit some results in this area. In
particular, we consider the case of two individuals, who start with the same
overall probability distribution but different private information, and then
take turns in updating their probabilities. We note convergence of the
announced probabilities to a limiting value, which may or may not be the same
as that based on pooling their private information.
