Fairness and efficiency in the subjective claims problem: A bargaining experiment

The well-known bankruptcy problem considers the situation of how the liquidation value of a bankrupt firm should be divided amongst its creditors when the sum of (publicly known)claims exceeds the liquidation value. If, however, such claims are not objectively measurable because contributions are in “different currencies”, it is not clear how to apply the rules thatemerged from studies on the bankruptcy problem, such as proportionality or constrained equal awards rule. We consider such a situation in which agents have subjective evaluations of their own and their partners’ claims. In an experimental study we elicit these subjective claims and compare three unanimity bargaining protocols in terms of how they aggregate the conflictingclaims.The three bargaining protocols compared are the offer variant of the unanimity bargaining procedure proposed by Shaked (as reported by Sutton, 1986), Torstensson's demand variant(Torstensson, 2005), and the exit variant proposed by Krishna and Serrano (Krishna &Serrano, 1996). The protocols are compared in three performance dimensions, efficiency asthe percentage cake size allocated, where the more of the cake is discounted the longer itt akes; allocative fairness as the perceived fairness of the allocation achieved; and procedural fairness as the perceived fairness of the procedure itself.In our experiment with a total of 594 participants, subjects first participate in a real effort task consisting of a general knowledge quiz. In this part of the experiment they are assigned to one of three different cohorts. From their relative performance within their cohort they earn points which they bring into a partnership. Each partnership is made of three partners from the three different cohorts, thus the contributions of the partners are not directly comparable.Subjects’ points determine the size of the cake that is to be distributed in the second part ofthe experiment. At the beginning of the second part, subjects are asked what they consider afair division of the cake. Afterwards they play one of the three above-mentioned bargaining games to determine the final division of the jointly produced cake. Lastly they rank the procedure on a scale concerning their fairness.Regarding procedural fairness we find that the offer variant gets a significantly higher rank than both the exit and the demand variant, where on average the latter is ranked worst.The offer variant also performs best in terms of allocative fairness; here, however, the exit variant is ranked worst. Furthermore, for all bargaining procedures we see a striking disparity between low and high contributors within groups. While there are no differences between the claims of high contributors and what their partners assigned to them as a fair share, low contributors claim significantly more than what others consider fair for them. Still, also in this respect, Shaked’s offer variant comes closest to the initial fairness judgment. Finally, each of the three bargaining protocols achieves well over 95 percent efficiency.