Simple Markovian Equilibria in Dynamic Spatial Legislative Bargaining

Abstract

The paper proves, by construction, the existence of Markovian equilibria in a model of dynamic spatial legislative bargaining. Players bargain over policies in an infinite horizon. In each period, a majority vote takes place between the proposal of a randomly selected player and the status-quo, the policy last enacted. This determines the policy outcome that carries over as the status-quo in the following period; the status-quo is endogenous. Proposer recognition probabilities are constant and discount factors are homogeneous. The construction relies on simple strategies determined by strategic bliss points computed by the algorithm we provide. A strategic bliss point is the policy maximizing the dynamic utility of a player with ample bargaining power. Relative to a bliss point, the static utility ideal, a strategic bliss point is a moderate policy. Moderation is strategic and germane to the dynamic environment; players moderate in order to constrain the future proposals of opponents. Moderation is a strategic substitute; when a player's opponents do moderate, she does not, and when they do not moderate, she does. We prove that the simple strategies induced by the strategic bliss points computed by the algorithm deliver a Stationary Markov Perfect equilibrium. Thus we prove its existence in a large class of symmetric games with more than three players and (possibly with slight adjustment) in any three-player game. Because the algorithm constructs all equilibria in simple strategies, we provide their general characterization, and we show their generic uniqueness. Finally, we analyse how the degree of moderation changes with changes in the model parameters, and we discuss the dynamics of the equilibrium policies.