The dynamics of political compromise

We characterize efficient self-enforcing divisions of political or economic surplus between two parties that interact repeatedly. The party in power can decide the allocation, and the parties' political strength changes according to a Markov process. We find that the share of the party currently in power depends not only on its current strength but also on whether it had previously been even stronger since it last came to power. We find that the constitutional supermajority requirements that attempt to constrain the use of power can counterproductively create less compromise.