“One Bite at the apple”: Legislative bargaining without replacement

To better understand the motivations behind the multilateral bargaining behaviors observed in the laboratory, I consider a modified many-player divide-the-dollar game in which players cannot propose again if they were randomly selected in one of the previous rounds but failed to provide an accepted proposal. This finite-horizon bargaining model without replacement captures the legislative process in which each legislator has only one opportunity to propose while the order of proposers is unknown. The unique symmetric subgame perfect equilibrium has several features that allow the transparent interpretation of experimental data. I find that proposers do not fully extract their rent, but the concern about inequity aversion is not a driving factor even in a myopic sense. Out-of-equilibrium observations suggest that retaliation and the fear thereof may be driving factors.