A model of a general parimutuel system: Characterizations and equilibrium selection

The authors formulate a model of a parimutuel system which considers a horse race with two horses. In the present model, the raceholder offers a rate of the total betting revenue in the first stage. In the second stage each bettor simultaneously decides whether to bet one unit of money on one horse or to withdraw, according to one’s win predictions for each horse. The authors assume that all bettor’s predictions are different and are common knowledge. They define some types of equilibria in the second stage game and give necessary and sufficient conditions for their existence. One equilibrium is selected as a solution for the second stage game. The authors also define a solution for the whole game by using this result. Finally, they analyze the relation between the solution and variance for the bettor predictions.