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

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  • Erhan Bayraktar
  • Alexander Munk

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.

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  • Erhan Bayraktar & Alexander Munk, 2016. "High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering," Papers 1605.03653, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1605.03653
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    4. Lorig, Matthew & Zhou, Zhou & Zou, Bin, 2021. "Optimal bookmaking," European Journal of Operational Research, Elsevier, vol. 295(2), pages 560-574.

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