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The average-of-awards rule for claims problems

Author

Listed:
  • Miguel Ángel Mirás Calvo

    (Universidade de Vigo, RGEAF)

  • Carmen Quinteiro Sandomingo

    (Universidade de Vigo)

  • Estela Sánchez-Rodríguez

    (CINBIO, Universidade de Vigo, SIDOR)

Abstract

Given a claims problem, the average-of-awards rule ( $${\text {AA}}$$ AA ) selects the expected value of the uniform distribution over the set of awards vectors. The $${\text {AA}}$$ AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the $${\text {AA}}$$ AA rule and a procedure to compute it in terms of the parameters that define the problem.

Suggested Citation

  • Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2022. "The average-of-awards rule for claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 863-888, November.
    • Handle: RePEc:spr:sochwe:v:59:y:2022:i:4:d:10.1007_s00355-022-01414-6
    DOI: 10.1007/s00355-022-01414-6
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    References listed on IDEAS

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    1. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    2. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    3. Julio Díaz & Peter Borm & Ruud Hendrickx & Marieke Quant, 2005. "A geometric characterisation of the compromise value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 483-500, July.
    4. Julio González-Díaz & Miguel Mirás Calvo & Carmen Sandomingo & Estela Rodríguez, 2015. "Monotonicity of the core-center of the airport game," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 773-798, October.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    7. Sergei Pechersky, 2015. "A note on external angles of the core of convex TU games, marginal worth vectors and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 487-498, May.
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    Cited by:

    1. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2023. "Refining the Lorenz‐ranking of rules for claims problems on restricted domains," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 526-558, September.

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