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Group Decision and Negotiation

Erschienen in:

01.05.2014

A Way to Play Claims Problems

verfasst von: José-Manuel Giménez-Gómez

Erschienen in: Group Decision and Negotiation | Ausgabe 3/2014

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Abstract

Commitment among agents is always difficult, especially when a scarce resource is to be shared. On the one hand, there are many possible ways to assign the available amount; on the other hand, each agent is motivated to propose a distribution that maximizes her award. In this paper, we propose a mechanism that combines the diminishing claims (Chun in Math Soc Sci 17(3):245–261, 1989) and the unanimous concessions (Herrero in Advances in economic design. Springer, Berlin, 2003) procedures, thereby obtaining a new justification of rules based on averaging.

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See Thomson (2003) for the formal definition of properties. See Section 6 for the definition of the Lorenz criterion.

The Talmud rule (Aumann and Maschler 1985) assigns the awards that \(CEA\) recommends for \((E, c/2)\), when the endowment is less than the half-sum of the claims. Otherwise, each agent receives her half-claim plus the amount provided by \(CEL\) when it is applied to the residual problem \((E-C/2,c/2)\).

See Bosmans and Lauwers (2011) and Thomson (2007) for the formal definition of properties and Lorenz comparisons.

Arin J (2007) Egalitarian distributions in coalitional models. Int Game Theory Rev 9(1):47–57CrossRef

Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy from the Talmud. J Econ Theory 36:195–213CrossRef

Bosmans K, Lauwers L (2011) Lorenz comparisons of nine rules for the adjudication of conflicting claims. Int J Game Theory 40:791–807CrossRef

Chun Y (1989) A noncooperative justification for egalitarian surplus sharing. Math Soc Sci 17(3):245–261CrossRef

Chun Y, Thomson W, Schummer J (2001) Constrained Egalitarianism: a new solution to bankruptcy problems. Seoul J Econ 14:269–297

Gadea-Blanco P, Giménez-Gómez JM, Marco-Gil MC (2010) Some game-theoretic grounds for meeting people half-way. IVIE. Working Papers, Serie AD 04

Garcia-Jurado I, Gónzalez-Villar A (2006) A non-cooperative approach to bankruptcy problems. Span Econ Rev 8:189–197CrossRef

Giménez-Gómez JM, Marco-Gil MC (2008) A new approach for bounding awards in bankruptcy problems. IVIE. Working Papers, Serie AD 07

Giménez-Gómez JM, Peris JE (2011) An axiomatic justification of mediation in bankruptcy problems. CREIP, Working Papers 18

Herrero C (2003) Equal awards versus equal losses: duality in bankruptcy problems. In: Sertel MR, Koray S (eds) Advances in economic design. Springer, Berlin, pp 413–426

Herrero C, Villar A (2001) The three musketeers: four classical solutions to bankruptcy problems. Math Soc Sci 42(3):307–328CrossRef

Lorenz M (1905) Methods of measuring the concentration of wealth. Publ Am Stat Assoc 9:209–219

Marco-Gil MC, Peris JE, Subiza B (1995). A mechanism for meta-bargaining problems. IVIE. Working Papers. Serie AD 98–17

Piniles HM (1861) Drkah shel Torah. Forester Edition, Viena

Rawls J (1971) A theory of justice. Belknap/Harvard, Cambridge

Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 6:19–31

Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45(3):249–297CrossRef

Thomson W (2007). On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach. Rev Econ Des 11(3):225–251

Thomson W, Yeh C (2008) Operators for the adjudication of conflicting claims. J Econ Theory 143(1): 177–198

van Damme E (1986) The Nash bargaining solution is optimal. J Econ Theory 38:78–100CrossRef

Titel: A Way to Play Claims Problems
verfasst von: José-Manuel Giménez-Gómez
Publikationsdatum: 01.05.2014
Verlag: Springer Netherlands
Erschienen in: Group Decision and Negotiation / Ausgabe 3/2014
Print ISSN: 0926-2644
Elektronische ISSN: 1572-9907
DOI: https://doi.org/10.1007/s10726-013-9347-5

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