A folk theorem for the one-dimensional spatial bargaining model

We show that in the one-dimensional bargaining model based on the protocol of Baron and Ferejohn (Am Polit Sci Rev 83:1181-1206, 1989), if voting is simultaneous, publicly observed, and no agent has the power to unilaterally impose a choice, then arbitrary policies can be supported by subgame perfect equilibria in stage-undominated voting strategies when agents are patient. Moreover, in the model with a bad status quo, arbitrary outcomes can be supported for arbitrary positive discount factors. We formulate sufficient conditions for supporting arbitrary alternatives in terms of a system of equations. The system has a straightforward solution in the model with no discounting, and after verifying non-singularity of this system, we use the implicit function theorem to derive the folk theorem when agents are sufficiently patient.