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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. 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.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
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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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