  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.

Optimization and Control;Probability;Economics