The Derby Game: An Ordering-based Colonel Blotto Game

The Colonel Blotto game and its variants are a common approach to study competitive allocation of interchangeable resources (e.g., soldiers, money, or votes). We introduce a new variant of Blotto, which we call the Derby game, to study competitive allocation of non-interchangeable resources, such as campaign surrogates in politics or skilled workers in companies, and analyze its Nash equilibria. While Derby games unsurprisingly admit no pure Nash equilibria, our main results surprisingly show that Nash equilibria generically exist where one player plays a pure strategy, and we give necessary and sufficient conditions for such equilibria.