Competition and Monopoly in the Market for Pari-mutuel Bets - a theoretical Approach

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Herbert Walther


An intertemporal state dependent expected utility model (generating S-shaped probability weighting by incorporating anticipated flows of utility from elation and disappointment) is used as a framework for analyzing the demand for various gambles. The analysis is extended to compare pari-mutuel bets under competitive and monopolistic conditions. The following conclusions can be drawn: (1) A monopoly fosters the `skeweness' of the pari-mutual bet: In equilibrium, the wager and the demand for probability to win are lower, while the wager per unit of probability to win and the prize are higher. (3) If prize expectations are endogenous, rollovers might be a necessary device to prevent instability. (4) Rational gamblers will be indifferent between `wager tax' and `bank holder' type methods of raising monopoly profits.I am grateful for helpful comments received from the participants at the `Conference on Gambling and Prediction Markets', organized by `Economica' and held at UCLA Riverside (20.-22 May 2007).

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