Limit Equilibria of Uni-Dimensional Bargaining Games: A Core Refinement

Abstract

In uni-dimensional policy space, the median voter theorem provides a unique equilibrium characterization under simple majority rule. But for general decision procedures, the core is generically non-unique. We make a selection from the core by taking the limit equilibrium of a standard bargaining game as players become perfectly patient. Our refinement is characterized by asymmetric Nash bargaining with endogenous bargaining weights, between two players whose identities depend on the decision rule. The limit policy often (but not always) coincides with the ideal policy of some agent, not necessarily the median. The model provides foundations for endogenous separation of agents into cohesive voting blocs represented by non-median factional leaders.