Repeated electoral competition over non-linear income tax schedules

We consider a repeated electoral competition game between two parties, each representing a constituent with a given income level. Parties are unable to commit to any policy before the election; they choose a non-linear income tax schedule once elected. In each period, citizens cast a vote either for the incumbent or for the challenger. We first show that there exist (pure strategy) subgame perfect equilibria where both parties choose the most-preferred tax schedule of their constituent, subject to the constraint that they are reelected. We characterize a specific class of these BPR (Best Policy with Reelection) equilibria in which one of the parties plays its constituent's unconstrained optimal tax function. Equilibrium tax schedules are always piecewise linear. Depending on the income levels of the two parties' constituents, we obtain either classical left-vs-right equilibria (where poorer people vote for one party and richer people for the other one) or ends-against-the-middle equilibria (where both poor and rich people vote for one party while the middle class vote for the other party). In both types of equilibria both parties propose the same tax schedule to a subset of the population.