A Blotto Game Approach to Ride-hailing Markets with Electric Vehicles

Abstract: When a centrally operated ride-hailing company considers to enter a market already served by another company, it has to make a strategic decision about how to distribute its fleet among different regions in the area. This decision will be influenced by the market share the company can secure and the costs associated with charging the vehicles in each region, all while competing with the company already operating in the area. In this paper, we propose a Colonel Blotto-like game to model this decision-making. For the class of games that we study, we first prove the existence and uniqueness of a Nash Equilibrium. Subsequently, we provide its general characterization and present an algorithm for computing the ones in the feasible set's interior. Additionally, for a simplified scenario involving two regions, which would correspond to a city area with a downtown and a suburban region, we also provide a method to check for the equilibria on the feasible set's boundary. Finally, through a numerical case study, we illustrate the impact of charging prices on the position of the Nash equilibrium.