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

Abstract

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.

Analysis of a Poisson-picking symmetric winners-take-all game with randomized payoffs

“…This would likely involve modeling the participants using several distinct sub-models, according to their goals (which might not necessarily be to maximize their expected income) and their level of sophistication. This approach is taken by the work in [BM17], which answers in the negative the question of whether a particular simple stratified model results in some of the phenomena that can be observed in real-life parimutuel games.…”

How to Play Fantasy Sports Strategically (and Win)

“…But it may be possible to solve very stylized versions of these DFS games where it is possible to purchase or sell short fractional amounts of athletes. There has been some success in solving mean-field games in the literature on parimutuel betting (Bayraktar and Munk 2017) in horse-racing and it may be possible to do likewise here for very stylized versions of DFS contests.…”