Bargaining over an endogenous agenda

We present a model of bargaining in which a committee searches over the policy space, successively amending the default by voting over proposals. Bargaining ends when proposers are unable or unwilling to amend the existing default, which is then implemented. Our main goal is to study the policies which can be implemented from any initial default in a pure strategy stationary Markov perfect equilibrium for an interesting class of environments including multi-dimensional and infinite policy spaces. It is convenient to start by characterizing the set of immovable policies: which are implemented, once reached as default. These policies form a weakly stable set; and conversely, any weakly stable set is supported by some equilibrium. Using these results, we show that minimum-winning coalitions may not form, and that a player who does not propose may nevertheless earn all of the surplus from agreement. We then consider how equilibrium outcomes change as we vary the order in which players propose, the identity of proposers, and the set of winning coalitions. First, if the policy space is well ordered then the committee implements the ideal policy of the last proposer in a subset of a weakly stable set; but this result does not generalize to other cases. We also show, surprisingly, that a player may prefer not to be given the opportunity to propose; and that the set of immovable policies may shrink as the quota increases. Finally, we derive conditions under which immovable policies in semi-Markovian equilibria form a consistent choice set.