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

• Miguel Ángel Mirás Calvo ^[1] ; Iago Núñez Lugilde ^[2] ; Carmen Quinteiro Sandomingo ^[1] ; Estela Sánchez-Rodríguez ^[1]
  1. [1] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
  2. [2] Universidade da Coruña

     Universidade da Coruña

     A Coruña, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 34, Nº. 1, 2026, págs. 102-135
• Idioma: inglés
• DOI: 10.1007/s11750-025-00704-3
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Aumann RJ (2010) Some non-superadditive games, and their Shapley values, in the Talmud. Int J Game Theory 39:3–10
  • Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213
  • Bosmans K, Lauwers L (2011) Lorenz comparisons of nine rules for the adjudication of conflicting claims. Int J Game Theory 40:791–807
  • Curiel IJ, Maschler M, Tijs SH (1987) Bankruptcy games. Z Oper Res 31(5):A143–A159
  • Dagan N (1996) New characterizations of old bankruptcy rules. Soc Choice Welfare 13(1):51–59
  • Grahn S, Voorneveld M (2002) Population monotonic allocation schemes in bankruptcy games. Ann Oper Res 109:317–329
  • Mirás Calvo MA, Quinteiro Sandomingo C, Sánchez Rodríguez E (2022) The average-of-awards rule for claims problems. Soc Choice Welfare 59:863–888
  • Mirás Calvo MA, Núñez Lugilde I, Quinteiro Sandomingo C, Sánchez Rodríguez E (2023a) Deviation from proportionality and Lorenz-domination...
  • Mirás Calvo MA, Núñez Lugilde I, Quinteiro Sandomingo C, Sánchez Rodríguez E (2023b) An operational toolbox for solving conflicting claims...
  • Mirás Calvo MA, Núñez Lugilde I, Quinteiro Sandomingo C, Sánchez Rodríguez E (2023c) Refining the Lorenz-ranking of rules for claims problems...
  • Núñez Lugilde I, Mirás Calvo MA, Quinteiro Sandomingo C, Sánchez Rodríguez E (2025) ClaimsProblems: Analysis of Conflicting Claims. R package...
  • O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371
  • Sprumont Y (1990) Population monotonic allocation schemes in for cooperative games with transferable utility. Games Econ Behav 2:378–394
  • Thomson W (2019) How to divide when there isn’t enough. From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation....