influence is a natural objective under plurality rules and political parties
locate their representatives in order to spread this influence. It is of partic-
ular interest in situations where voters have but a small cost of voting in
which case it is hard to justify voter participation and several papers try to
explain large voter turnouts by assuming that parties are able to influence
individual voters to join ideological groups. As put in Martinelli and Her-
rera [2006], voters are to belong to groups and groups are formed by leading
party activists (see also for example Shachar and Nalebuff [1999] and Coate
and Conlin [2004]). While Martinelli and Herrera [2006] extend the existing
literature on how parties influence voters by forming groups through group
leaders to the case where these leader arrive endogenously from the popu-
lation, the game we study can be applied to situations where two existing
parties locate respective party leaders across the electorate to do the same.
With such objectives, it is important to find specifically a winning or tying
strategy for a player.
A recent work in this respect is a game of influence studied by Ahn et al.
[2004], where there are two players (firms or political parties) who are each
endowed with the same number of facilities (resources to set up a number
of shops or finance a number of party leaders) to locate (possibly in batches
of more than one facilities) on a circle in a sequential manner. In order to
win the game, a player must try to secure as much area as possible that
is closer to its locations than those of its competitor. Each player faces a
resource mobility constraint such that not all facilities can be located in the
first round. They show that in such a game (to be described precisely in
section 2) where play must involve at least two rounds, the second mover
always has a winning strategy and the game would always result in a tie
if players were forced to end the game in a single round. In Cheong et al.
[2002] the existence of a winning strategy for the second mover is shown,