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

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.

Modular best proximity and equilibrium pairs in free generalized games

In this paper, we prove a fixed point theorem for ?-acyclic factorizable multifunction. Some existence theorems of general best proximity pairs and equilibrium pairs are presented in modular function spaces. Moreover, some equilibrium theorems are established for free generalized n-person game.