We study a legislative bargaining game in which failure to agree in a given round may result in a breakdown of negotiations. In that case, each player receives an exogenous `disagreement value'. We characterize the set of stationary subgame perfect equilibria under all q-majority rules. Under unanimity rule, equilibrium payoffs are strictly increasing in disagreement values. Under all less-than-unanimity rules, expected payoffs are either decreasing or first increasing and then decreasing in disagreement values. We conduct experiments involving three players using majority and unanimity rule, finding support for these predictions.
legislative bargaining majority rule unanimity rule risk of breakdown experiments