We consider a model of two-party electoral competition where the parties seek to maximize expected vote shares. The parties form expectations based on possibly different beliefs about the profile of the ideal policies for voters. The model has a Nash equilibrium only under the knife-edge condition that the two parties’ beliefs about the ideal policy for a “random voter” (i.e., a voter who is picked uniformly at random from the electorate) have equal medians; at the equilibrium they choose this median policy as their platforms. Approximate equilibria, defined as pairs of platforms that are almost best responses to each other, may exist even in the absence of a Nash equilibrium. We show that at the approximate equilibria, the parties adopt close platforms, and have opposite “estimates” about the random voter’s ideal policy. We also show that if the policy space has several dimensions, and if the parties’ beliefs are close enough, then typically approximate equilibria do not exist.
ASJC Scopus subject areas
- Economics and Econometrics
- Social Sciences (miscellaneous)