A Location Game On Disjoint Circles

Abstract

Two players are endowed with resources for setting up N locations on K
identical circles, with N > K ≥ 1. The players alternately choose these
locations (possibly in batches of more than one in each round) in order to
secure the area closer to their locations than that of their rival’s. They face
a resource mobility constraint such that not all N locations can be placed in
the first round. The player with the highest secured area wins the game and
otherwise the game ends in a tie. Earlier research has shown that for K = 1,
the second mover always has a winning strategy in this game. In this paper
we show that with K > 1, the second mover advantage disappears as in this
case both players have a tying strategy. We also study a natural variant
of this game where the resource mobility constraint is more stringent so
that in each round each player chooses a single location where we show that
the second mover advantage re-appears. We suggest some Nash equilibrium
configurations of locations in both versions of the game.

Keywords: Competitive locations, Disjoint spaces, Winning/Tying strate-
gies, Equilibrium configurations.

JEL Classification: C72, D21, D72.

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