Implicit coordination in an <inline-formula><tex-math id="M1">$ n $</tex-math></inline-formula>-player target selection game

Abstract

We show that a class of target selection games has a unique symmetric mixed strategy Nash equilibrium $ x^\ast $. We also present a simple recursion that computes $ x^\ast $ within a finite number of iterations. Along the way, we introduce the concept of value compactness that points directly to the properties of the unique symmetric mixed strategy equilibrium, including the fact that the unique equilibrium does not force any player to make an arbitrary decision about associating positive probability with subsets of targets having a particular utility– a property that we refer to as implicit coordination.