Parimutuel betting under asymmetric information

Abstract

This paper examines simple parimutuel betting games under asymmetric information, with particular attention to differences between markets in which bets are submitted simultaneously versus sequentially. In the simultaneous parimutuel betting market, all (symmetric and asymmetric) Bayesian-Nash equilibria are generically characterized as a function of the number of bettors and the quality of their private information. There always 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 sequential framework, earlier bets have information externalities, because they may reveal private information of bettors. They also have payoff externalities, because they affect the betting odds. One effect of these externalities is that the separating equilibrium disappears if the number of betting periods is sufficiently large

Noise, Information, and the Favorite-Longshot Bias in Parimutuel Predictions

“…For example, the pool could be divided equally among all active bettors. 20 Koessler, Noussair, and Ziegelmeyer (2008) note that there also may be asymmetric equilibria when N is small. explicitly compute the expected payment, W k , as a function of the betting probabilities…”

“…The …rst game-theoretic analysis of parimutuel markets with private information is by Frédéric Koessler, Charles Noussair, and Anthony Ziegelmeyer (2008). They construct equilibria when bettors have binary signals.…”

Information Aggregation and Beliefs in Experimental Parimutuel Betting Markets

“…The sequential parimutuel betting game we study in our experiment is a well-defined extensive form game, and in principle, Nash or sequential equilibria can be identified, although this is an intractable exercise due to the enormous potential number of strategy profiles (see Koessler, Noussair, and Ziegelmeyer, 2007). However, there are two difficulties with using sequential equilibrium or any weaker equilibrium concept as a predictive tool for this game.…”

High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering

“…Signi¯-cant attention has been paid to strategic interactions among bettors E. Bayraktar & A. Munk (Quandt, 1986;Terrell and Farmer, 1996;Plott et al, 2003;Koessler et al, 2008;Ottaviani and Sørensen, 2009).…”

“…Watanabe, Nonoyama, and Mori's setup and goals are similar to those in Watanabe's continuum game paper, except that the di®use players in the latter are replaced by¯nitely many atomic players (Watanabe et al, 1994;Watanabe, 1997). Explanations of the favorite-longshot bias have been o®ered using equilibrium results for N -player parimutuel wagering games (Chadha and Quandt, 1996;Potters and Wit, 1996;Koessler et al, 2008;Ottaviani and Sørensen, 2009). Games in which¯nitely many bettors wager sequentially have also been investigated for various purposes (Thrall, 1955;Cheung, 1985;Feeney and King, 2001;Koessler et al, 2003Koessler et al, , 2008.…”