Nash equilibrium structure of Cox process Hotelling games

Abstract We study an N -player game where a pure action of each player is to select nonnegative function on Polish space supporting finite diffuse measure, subject constraint the integral function. This used define intensity Poisson point process space. The processes are independent over players, and value measure union her open Voronoi cells in superposition process. Under randomized strategies, points thus Cox process, nature competition between players akin that Hotelling games. characterize when such admits Nash equilibria prove equilibrium exists, it unique consists strategies proportional same proportions as total intensities. give examples games do not exist. A better understanding criterion for existence remains intriguing problem.