A Location Game On Disjoint Circles



even for a single round location game played on a two dimensional closed
plane. In Chawla et al. [2003] an upper bound for the size of the first mover
disadvantage is provided in a game where firms compete to maximize market
shares and consumers are distributed over a d-dimensional Euclidean space.

A variant of the the above mentioned games of influence is where players
compete over a collection of disjoint areas in which locations can be placed.
To the best of our knowledge, this variant has not been studied so far and
there are many real life situations that suggest its importance. For example,
retail chains set up stores in different cities or countries. In politics, these
disjoint areas can represent different sections of the citizens with distinct
group-identities (like workers, students, or simply electorally disconnected
geographic neighbourhoods like districts and states) and to set up locations
in a given region can be viewed as an attempt by the political parties to open
political units (like politically motivated trade unions, district party offices
or students unions in academic institutions wth designated leaders) to spread
influence among target groups and increase favorable voter participation.
This paper adresses such location games on disjoint areas by extending Ahn
et al. [2004] to a family of disjoint circles. In what follows we shall abstract
away from parties and firms and simply refer to them as players. We are
not interested in studying any particular model in politics or industry, but
rather analyze the issue of stratgic influence in abstract. It is also important
to mention that all our results can be easily extended to any closed curves
rather than just circles.

We show that the second mover advantage as in Ahn et al. [2004] disap-
pears and the first mover always has a tying strategy. We also show that in
any Nash equilibrim of the game, there must be a tie. We then extend this
game by making the resource mobility constraint more stringent so that in
each round, each player places exactly one location. In this extended game



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