A PARIMUTUEL SYSTEM WITH 2 HORSES AND A CONTINUUM OF BETTORS

In this paper we study a model of a parimutuel system described as a h orse race with two horses and many betters. Each better predicts which horse will win and the raceholder maximizes his revenue-taking from a ll bets. After an announcement of raceholder's revenue rate for subtra cting all betting money, all betters simultaneously decide their behav iors among three strategies, betting one unit of money on either of ho rses or withdrawing. The game at second stage which is main interests of our study is a game in normal forms with a continuum of players. We show that there exists an equilibrium in which sets of betters bettin g on two horses are not null sets, if the rate of raceholder's revenue is not large. The equilibrium is always regular in the sense that any betters whose probabilities for win of a horse is larger than someone s' betting on the horse must bet on the horse. The equilibrium is dete rmined up to equivalence for null sets, when any better's prediction i s different from the other's one. Some numerical examples are shown.