On how the rules that extend the concede-and-divide principle differ for pairs of claimants

Abstract In the context of conflicting claims problems, the Talmud, adjusted proportional, random arrival, minimal overlap, and average-of-awards rules are well-known extensions of the two-claimant concede-and-divide rule to larger populations. We analyze how the awards recommended by these rules for each couple of claimants differ from what they would receive if the concede-and-divide principle were applied to distribute among them their joint payoff. To compare the behavior of these rules for pairs of claimants, we rely on geometric features of the corresponding two-dimensional paths of awards. We study properties pertaining to the impact, in absolute and relative terms, that one claimant leaving the problem has on the awards of the remaining claimants.