Balance of power and divergence of policies in a model of electoral competition

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. In an equilibrium the two incumbents choose to prevent the entry and achieve the balance of power, i.e., splitting the electorate equally. The incumbents' positions might diverge more as compared to a system in which the parties seek to solely maximize the voters' support. Therefore, rank preoccupation under the threat of entry might contribute to more polarized political platforms of the two leading parties.