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Transversality of the Shapley value

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  • Stefano Moretti

    ()

  • Fioravante Patrone

    ()

Abstract

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Suggested Citation

  • Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
  • Handle: RePEc:spr:topjnl:v:16:y:2008:i:1:p:1-41
    DOI: 10.1007/s11750-008-0044-5
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    File URL: http://hdl.handle.net/10.1007/s11750-008-0044-5
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    References listed on IDEAS

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    1. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Suijs, Jeroen & Borm, Peter, 1999. "Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents," Games and Economic Behavior, Elsevier, vol. 27(2), pages 331-345, May.
    5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    6. Stefano Moretti & Fioravante Patrone & Stefano Bonassi, 2007. "The class of microarray games and the relevance index for genes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 256-280, December.
    7. Vladislav Kargin, 2003. "Uncertainty of the Shapley Value," Game Theory and Information 0309003, University Library of Munich, Germany.
    8. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    9. Judith Timmer & Peter Borm & Stef Tijs, 2004. "On three Shapley-like solutions for cooperative games with random payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 595-613, August.
    10. Mertens, Jean-Francois, 2002. "Some other economic applications of the value," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 58, pages 2185-2201 Elsevier.
    11. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    12. Hart, Sergiu, 2002. "Values of perfectly competitive economies," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 57, pages 2169-2184 Elsevier.
    13. Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167 Elsevier.
    14. repec:spr:lnecms:978-3-540-28509-0 is not listed on IDEAS
    15. Young, H.P., 1994. "Cost allocation," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 34, pages 1193-1235 Elsevier.
    16. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, November.
    17. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    18. Paula González & Carmen Herrero, 2004. "Optimal sharing of surgical costs in the presence of queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 435-446, July.
    19. Vazquez-Brage, M. & van den Nouweland, A. & Garcia-Jurado, I., 1997. "Owen's coalitional value and aircraft landing fees," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 273-286, October.
    20. repec:dau:papers:123456789/4952 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Alcalde, Jose & Marco-Gil, María del Carmen & Silva, José A., 2010. "Merging and Going Bankrupt: A Neutral Solution," MPRA Paper 28339, University Library of Munich, Germany.
    2. José M. Jiménez Gómez & María del Carmen Marco Gil & Pedro Gadea Blanco, 2010. "Some game-theoretic grounds for meeting people half-way," Working Papers. Serie AD 2010-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Karl Michael Ortmann, 2016. "The link between the Shapley value and the beta factor," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 311-325, November.
    4. repec:eee:gamebe:v:108:y:2018:i:c:p:93-112 is not listed on IDEAS
    5. repec:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0660-1 is not listed on IDEAS
    6. Perea, Federico & Puerto, Justo & Fernández, Francisco R., 2012. "Avoiding unfairness of Owen allocations in linear production processes," European Journal of Operational Research, Elsevier, vol. 220(1), pages 125-131.
    7. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    8. Roberto Lucchetti & Stefano Moretti & Fioravante Patrone, 2015. "Ranking sets of interacting objects via semivalues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 567-590, July.
    9. Roberto Roson & Franz Hubert, 2015. "Bargaining Power and Value Sharing in Distribution Networks: A Cooperative Game Theory Approach," Networks and Spatial Economics, Springer, vol. 15(1), pages 71-87, March.
    10. Vito Fragnelli & Josep Freixas & Montserrat Pons & Lluís Sanmiquel, 2016. "Measuring the relevance of factors in the occurrences of events," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(3), pages 535-561, September.
    11. Joaquín Sánchez-Soriano, 2008. "Comments on: Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 54-57, July.
    12. Aguilera, Néstor E. & Di Marco, Silvia C. & Escalante, Mariana S., 2010. "The Shapley value for arbitrary families of coalitions," European Journal of Operational Research, Elsevier, vol. 204(1), pages 125-138, July.
    13. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    14. Stefano Moretti & Fioravante Patrone & Ariel Dinar & Safwat Abdel-Dayem, 2016. "Sharing the Costs of Complex Water Projects: Application to the West Delta Water Conservation and Irrigation Rehabilitation Project, Egypt," Games, MDPI, Open Access Journal, vol. 7(3), pages 1-23, July.
    15. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    16. M. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. Mosquera, 2012. "Cost allocation in inventory transportation systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 397-410, July.
    17. José Alcalde & María Carmen Marco-Gil & José Silva-Reus, 2014. "The minimal overlap rule: restrictions on mergers for creditors’ consensus," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 363-383, April.

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