We prove existence of stationary Markov perfect equilibria in an infinite horizon model of legislative bargaining in which the policy out come in one period determines the status quo in the next. We allow for a multidimensional policy space and arbitrary smooth stage utilities. We prove that all such equilibria are essentially in pure strategies and that proposal strategies are differentiable almost everywhere. The model is general enough to accommodate much of the institutional structure observed in real-world legislatures and parliaments.
Political interaction in modern democracies qualifies as one of the most complex phenomena subjected to scientific inquiry. The need to accommodate this complexity in formal political theory models stems not only from the desire to sate our intellectual curiosity, but seems also essential for the analysis of the effects of public policy and the design of constitutions. In this spirit we seek to develop a class of models of policy making that (i) accounts for the multidimensional nature of public policy, (ii) captures the continuing nature of policy over time, (iii) is rich enough to reflect institutional structure at a fine level of detail, and (iv) allows for the kinds of random shocks (e.g.,on preferences and the social environment) to which political interaction is subjected over time. The political economy literature to date has had limited success in addressing these issues. At a formal level, the primary difficulty that arises is the existence of equilibria in which policy makers use relatively simple and intuitive strategies. Beyond that is the problem of characterizing equilibria, once they are known to exist, and finally there is the task of applying the model, i.e., developing useful special cases and, when the limits of formal analysis are reached, bringing numerical techniques to bear.
We lay the theoretical foundations for such future applications by es-tablishing the existence of stationary Markov perfect equilibria in a class of models with the desiderata (i)–(iv) identified above, and we show that in every such model equilibria are essentially in pure strategies, and legislators’ proposal strategies are differentiable almost everywhere. We consider an infinite-horizon model of legislative bargaining where each period begins with the random draw of a legislator, who proposes any feasible policy, which is then subject to a majority vote. In this respect, our protocol is familiar from the Baron-Ferejohn (1989) model of distributive bargaining in the political science literature. In their work, however, the game ends with the proposed allocation of surplus if a majority of legislators accept the proposal; otherwise, all agents receive a payoff of zero, and the bargaining game is repeated in the next period. Thus, that model is appropriate for examining policy choices across legislative sessions only if policies remain in place for a single session, with an exogenously fixed default outcome in every future session in which a new agreement is not reached. This is often the case, for example, in budgetary negotiations. The model is inadequate, however, for the analysis of continuing programs or legislation, where policy choices remain in place in the future, determining the status quo in future negotiations. In such environments, policy-makers must not only consider the impact of a policy proposal on the present, but also the future policies that would follow that choice.