IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v52y2018i1d10.1007_s10614-017-9673-9.html
   My bibliography  Save this article

On the Allocation of Multiple Divisible Assets to Players with Different Utilities

Author

Listed:
  • Ephraim Zehavi

    (Bar-Ilan University)

  • Amir Leshem

    (Bar-Ilan University)

Abstract

When there is a dispute between players on how to divide multiple divisible assets, how should it be resolved? In this paper we introduce a multi-asset game model that enables cooperation between multiple agents who bargain on sharing K assets, when each player has a different value for each asset. It thus extends the sequential discrete Raiffa solution and the Talmud rule solution to multi-asset cases.

Suggested Citation

  • Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9673-9
    DOI: 10.1007/s10614-017-9673-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-017-9673-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-017-9673-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Trockel, Walter, 2011. "An axiomatization of the sequential Raiffa solution," Center for Mathematical Economics Working Papers 425, Center for Mathematical Economics, Bielefeld University.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 287-297, November.
    4. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    5. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    6. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    7. Trockel, Walter, 2014. "Robustness of intermediate agreements for the discrete Raiffa solution," Games and Economic Behavior, Elsevier, vol. 85(C), pages 32-36.
    8. Amparo Mármol & Clara Ponsatí, 2008. "Bargaining over multiple issues with maximin and leximin preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 211-223, February.
    9. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    10. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    11. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    12. Salonen, Hannu, 1988. "Decomposable solutions for N -- person bargaining games," European Journal of Political Economy, Elsevier, vol. 4(3), pages 333-347.
    13. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    14. Emily Tanimura & Sylvie Thoron, 2008. "A mechanism for solving bargaining problems between risk averse players," Working Papers halshs-00325695, HAL.
    15. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    16. William Thomson, 2013. "Game-Theoretic Analysis Of Bankruptcy And Taxation Problems: Recent Advances," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    17. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    18. Quant, Marieke & Borm, Peter & Hendrickx, Ruud & Zwikker, Peter, 2006. "Compromise solutions based on bankruptcy," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 247-256, May.
    19. van Damme, E.E.C. & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Other publications TiSEM 4bd5eb9e-328a-45a0-aa0a-e, Tilburg University, School of Economics and Management.
    20. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    21. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    22. Zvi A. Livne, 1989. "Axiomatic Characterizations of the Raiffa and the Kalai-Smorodinsky Solutions to the Bargaining Problem," Operations Research, INFORMS, vol. 37(6), pages 972-980, December.
    23. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    24. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    25. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "Balanced Contributions for Multi-Issue Allocation Situations," Discussion Paper 2005-93, Tilburg University, Center for Economic Research.
    26. M. Hinojosa & A. Mármol & F. Sánchez, 2012. "A consistent talmudic rule for division problems with multiple references," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 661-678, October.
    27. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    28. 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.
    29. Claus-Jochen Haake, 2009. "Dividing By Demanding: Object Division Through Market Procedures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 15-32.
    30. Clara Ponsati & Joel Watson, 1998. "Multiple-Issue Bargaining and Axiomatic Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(4), pages 501-524.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    2. Walter Trockel, 2015. "Axiomatization of the discrete Raiffa solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 9-17, April.
    3. Emily Tanimura & Sylvie Thoron, 2016. "How Best to Disagree in Order to Agree?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-17, September.
    4. Bram Driesen & Peter Eccles & Nora Wegner, 2017. "A non-cooperative foundation for the continuous Raiffa solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1115-1135, November.
    5. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB School of Economics Working Papers 2016/347, University of Barcelona School of Economics.
    6. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.
    7. Gustavo Bergantiños & Jose María Chamorro & Leticia Lorenzo & Silvia Lorenzo‐Freire, 2018. "Mixed rules in multi‐issue allocation situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 66-77, February.
    8. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 603-622, August.
    9. Sinan Ertemel & Rajnish Kumar, 2018. "Proportional rules for state contingent claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 229-246, March.
    10. José-Manuel Giménez-Gómez & António Osório & Josep E. Peris, 2015. "From Bargaining Solutions to Claims Rules: A Proportional Approach," Games, MDPI, vol. 6(1), pages 1-7, March.
    11. Juan D. Moreno-Ternero, 2017. "A Talmudic approach to bankruptcy problems," LIDAM Reprints CORE 2914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    13. J. Sánchez-Pérez, 2023. "New results for multi-issue allocation problems and their solutions," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 313-336, June.
    14. M. Hinojosa & A. Mármol & F. Sánchez, 2013. "Extended proportionality in division problems with multiple references," Annals of Operations Research, Springer, vol. 206(1), pages 183-195, July.
    15. Harless, Patrick, 2017. "Wary of the worst: Maximizing award guarantees when new claimants may arrive," Games and Economic Behavior, Elsevier, vol. 105(C), pages 316-328.
    16. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    17. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    18. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    19. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    20. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9673-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.