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 between fully 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 always exists a separating equilibrium, where all bettors follow their private signal. This equilibrium becomes 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 equilibrium disappears 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 the interaction between information externalities generated by observational learning and payoff externalities generated by betting odds, bettors arbitrate between following their private signal, following the choices of previous bettors, and betting against the trend. Extreme effects based on herd behavior occur in identifiable states of the world, leading to significant short run mispricing