Parimutuel Betting under Asymmetric Information

This paper examines simple parimutuel betting games under asymmetric information,with particular attention to differences between markets in which bets are submittedsimultaneously versus sequentially. In the simultaneous parimutuel betting market, all(symmetric and asymmetric) Bayesian-Nash equilibria are generically characterized as afunction of the number of bettors and the quality of their private information. Therealways exists a separating equilibrium, in which all bettors follow their private signals.This equilibrium is unique if the number of bettors is sufficiently large. In the sequentialframework, earlier bets have information externalities, because they may reveal privateinformation of bettors. They also have payoff externalities, because they affect the bettingodds. One effect of these externalities is that the separating equilibrium disappears if thenumber of betting periods is sufficiently large.