Legislative bargaining with heterogeneous disagreement values: Theory and experiments

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 qualitative support for several, but not all, of our main predictions. Having a high disagreement value is indeed an advantage under unanimity rule. Under majority rule, the player with the highest disagreement value is more likely to be excluded, but this does not consistently result in a lower average payoff.