A purely non-cooperative model of divided government

In this paper I describe an institutional structure in which there are two branches of the government: the executive one, elected by plurality rule, and the legislative one elected by proportional rule. The resulting policy outcome is described through a compromise between these two branches. Given the presidential result, legislative elections are characterized by essentially an unique Nash equilibrium such that any voter on the left of the corresponding policy outcome votes for the leftist party and any voter on the right votes for the rightist party. Moreover, this equilibrium can be obtained by a process of iterated elimination of dominated strategies. The whole game is then solved by backward induction and dominance arguments.