A Location Game On Disjoint Circles

1 Introduction

The possibility and practice of choosing locations competitively in order
to maximize influence over sources that generate payoffs is widespread in
economics and politics. For example, retail firms compete over geographic
location of chain stores in order to capture a larger share of the market.
Political parties may set up party-offices or affiliated bodies in order to
spread political influence over the electorate. In such situations, the ability
of players to maximize influence by choosing locations may depend upon
the order in which such locations are chosen, thereby bringing up issues
concerning the first and second mover advantages.

Games involving choice of locations has long been an important area of
study in economics. The corresponding literature centers around the seminal
work by Hotelling [1929] which considers a profit maximizing firm’s decision
about optimal location when the consumers are located uniformly on a line
segment. Subsequently, this was extended to the celebrated circular city
model in Chamberlin [1953] and later by Salop [1979]. While in Hotelling
[1929], Chamberlin [1953] and Salop [1979] simultaneous-move games are
considered, Prescott and Visscher [1977] and Economides [1986] study the
problem when firms are allowed to enter sequentially on a line segment and
circular city respectively to show that the outcomes of a sequential location
game can differ significantly from those obtained in a simultaneous-move
scenario.

In some environments involving location games, players may have the
sole objective of being the one with the highest influence, as for example, in
a competition to win the race for establishing its product as the standard
product in the market, a firm may set shops to acquire patronage from a
majority of customers (like popularizing a software) which may then have
long term benefits for the firm. In politics, having the highest ideological

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