Adv. Math. Econ. 10, 101-119 (2007)

Existence and uniqueness of an equilibrium in a model of spatial electoral competition with entry

Anna Rubinchik^{1} and Shlomo Weber^{2}

1 Department of Economics, University of Colorado at Boulder, UCB 256, Boulder, CO 80309, USA

2 SMU, Department of Economics, Dallas, TX, USA CORE, Catholic University of Louvain, Louvain, Belgium CEPR, London, UK

Received: October 3, 2006 Revised: October 3, 2006

JEL classification: C62, C72, D72

Mathematical Subject Classification (2000): 91A10, 91B12

Abstract. Two incumbent parties choose their platforms in a unidimensional policy space while facing a credible threat of an entry by the third party. Relative electoral support is the predominant objective of each party, and the third party enters only if it can displace one of the incumbents by receiving at least the second highest support. We prove the existence and uniqueness of an equilibrium for a wide class of distributions of voters’ ideal points, including, in particular, log-concave distribution functions. Moreover, in an equilibrium the incumbents prevent the entry and achieve the “balance of power” by choosing distinct positions in the policy space and equally splitting the electorate.

Key words: incumbent parties, threat of entry, entry-deterrence, rank concerns, balance of power