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

TL;DR

This paper develops a generalized game-theoretic model to analyze how large-scale participants influence outcomes in parimutuel wagering, revealing complex effects on the house and bettors.

Contribution

It introduces a novel large generalized game model for parimutuel wagering, providing conditions for equilibrium existence and uniqueness, and analyzing real-world scenarios.

Findings

Large players can benefit the house under certain conditions.

Effects of large players are context-dependent and not always predictable.

The model offers nuanced insights into large-scale wagering impacts.

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.