Location games with references

TL;DR

This paper analyzes location games where players choose positions to attract resources, considering costs for deviating from reference points, with a focus on duopoly and multi-player competition, revealing conditions for equilibrium existence and structure.

Contribution

It provides a complete characterization of equilibria in location games with reference points, including existence, uniqueness, and structure for duopoly and multi-player cases.

Findings

Unique equilibrium depends on reference locations.

Equilibrium may involve no differentiation or full differentiation.

In multi-player games, only extreme players deviate from references.

Abstract

We study a class of location games where players want to attract as many resources as possible and pay a cost when deviating from an exogenous reference location. This class of games includes political competitions between policy-interested parties and firms' costly horizontal differentiation. We provide a complete analysis of the duopoly competition: depending on the reference locations, we observe a unique equilibrium with, or without differentiation, or no equilibrium. We extend the analysis to a competition between an arbitrary number of players and we show that there exists at most one equilibrium which has a strong property: only the two most-left and most-right players deviate from their reference locations.