Dynamic legislative policy making

We prove existence of stationary Markov perfect equilibria in an infinite-horizon model of legislative policy making in which the policy outcome in one period determines the status quo for the next. We allow for a multidimensional policy space and arbitrary smooth stage utilities, and we assume preferences and the status quo are subject to arbitrarily small shocks. We prove that equilibrium continuation values are differentiable and that proposal strategies are continuous almost everywhere. We establish upper hemicontinuity of the equilibrium correspondence, and we provide weak conditions under which each equilibrium of our model determines an aperiodic transition probability over policies. We establish a convergence theorem giving conditions under which the invariant distributions generated by stationary equilibria must be close to the core in a canonical spatial model. Finally, we extend the analysis to sequential move stochastic games and to a version of the model in which the proposer and voting rule are determined by play of a finite, perfect information game.