Parimutuel Betting under Asymmetric Information

This paper examines ¯nite parimutuel betting games with asymmetric information, with par-ticular attention to di®erences between sequential and simultaneous settings, and betweenfully rational and myopic (\price taking") behavior. In the simultaneous parimutuel market,all (symmetric and asymmetric) Bayesian-Nash equilibria are generically characterized de-pending on the number of bettors and the quality of their private information. There alwaysexists a separating equilibrium, where all bettors follow their private signal. This equilibriumbecomes unique as the number of bettors increases, and it corresponds to the strategy pro-¯le used by myopic bettors. In the sequential framework, the perfectly revealing equilibriumdisappears as the number of betting periods increases, whether or not bettors fully antici-pate their impact on future odds. In both cases (rational and myopic betting), due to theinteraction between information externalities generated by observational learning and payo®externalities generated by betting odds, bettors arbitrate between following their private sig-nal, following the choices of previous bettors, and betting against the trend. Extreme e®ectsbased on herd behavior occur in identi¯able states of the world, leading to signi¯cant shortrun mispricing.