Parimutuel Betting under Asymmetric Information

This paper examines finite parimutuel betting games with asymmetric information, with particular attention to differences 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 depending 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 profile used by myopic bettors. In the sequential framework, the perfectly revealing equilibriumdisappears as the number of betting periods increases, whether or not bettors fully anticipate their impact on future odds. In both cases (rational and myopic betting), due to theinteraction between information externalities generated by observational learning and payoffexternalities generated by betting odds, bettors arbitrate between following their private signal, following the choices of previous bettors, and betting against the trend. Extreme effectsbased on herd behavior occur in identifiable states of the world, leading to significant short run mispricing.