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

30 Pages Posted: 14 May 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Alexander Munk

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: May 11, 2016

Abstract

How do large-scale participants in parimutuel wagering events affect the house and ordinary bettors? A standard narrative suggests that they may temporarily benefit the former at the expense of the latter. To approach this problem, we begin by developing a model based on the theory of large generalized games. Constrained only by their budgets, a continuum of diffuse (ordinary) players and a single atomic (large-scale) player simultaneously wager to maximize their expected profits according to their individual beliefs. Our main theoretical result gives necessary and sufficient conditions for the existence and uniqueness of a pure-strategy Nash equilibrium. Using this framework, we analyze our question in concrete scenarios. First, we study a situation in which both predicted effects are observed. Neither is always observed in our remaining examples, suggesting the need for a more nuanced view of large-scale participants.

Keywords: parimutuel wagering, large generalized games, nash equilibrium

Suggested Citation

Bayraktar, Erhan and Munk, Alexander, High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering (May 11, 2016). Available at SSRN: https://ssrn.com/abstract=2778882 or http://dx.doi.org/10.2139/ssrn.2778882

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Alexander Munk

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109
United States

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