The “German Vote” and its consequences: (Un)reliable parties in multilateral bargaining under private information

Abstract

This paper theoretically investigates the strategic implications of varying reliability of bargaining partners under unanimous and non-unanimous voting. In a sequential two-period model, three players (one proposer, two responders) bargain over the distribution of a pie. One responder has private information about his valuation of finding an agreement, implying signaling values that differ substantially between voting rules and are affected by the other responder’s reliability. The other responder is of a non-strategic “robot” type, who is unreliable in the sense that in the first period, he may vote “no” after announcing a “yes”-vote. Under unanimity rule, the responder with private information benefits from voting “no” because this signals that he requires a larger compensation in a future period. In contrast, under majority rule, voting “no” is unattractive due to the fear of being excluded from a future coalition. Under both voting rules, one responder becoming less reliable negatively affects the other responder’s willingness to vote “yes”, making efficient agreements increasingly difficult to achieve. Under majority rule, the presence of unreliable parties can lead to more parties being included in the winning coalition, as demonstrated by an extension of the model. However, some of these insights are contingent on the specific assumptions of the model.