Nash equilibrium and party polarization in an electoral model with mixed motivations

We study the existence problem of Nash equilibrium as well as the patterns of equilibrium policy outcomes in an electoral competition model with mixed motivations. Each party maximizes a sum of party members’ expected utility and office rent. The inclusion of office rent renders the payoff of each party discontinuous. This makes it difficult to apply usually fixed point arguments to prove the existence of Nash equilibria. By using a recently developed concept, multiple restrictional security (MR-security) we provide conditions under which a pure-strategy Nash equilibrium exists within fairly general settings, and further the analysis by presenting conditions under which various patterns of policy choices, including polarization, arise in equilibrium.