Location Choice under Spillovers

This paper introduces the location choice under spillovers game: A number of firms choose from among a number of alternative locations. A firm's payoff at some location is the sum of two factors: Its location-specific idiosyncratic payoff; and the positive spillover it receives, which is a function of the number of firms choosing the same location. The spillover function is location-specific and monotonically increasing. This game form can be viewed as an extension of the classic “battle of sexes” game. It can also be used to model real-life game-theoretic situations with network effects, such as when app users choose from alternative social media or instant messaging apps. In our main result, we show that the location choice under spillovers game is a potential game, and hence, it always admits a Nash equilibrium in pure strategies. We also show that: A Nash equilibrium outcome need not be Pareto efficient. An outcome that is Pareto efficient need not be a Nash equilibrium. And a Nash equilibrium is not necessarily a strong equilibrium.