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Transversality of the Shapley value

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  • Stefano Moretti
  • Fioravante Patrone

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  • 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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    4. 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.
    5. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, September.
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    7. 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.
    8. 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.
    9. 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.
    10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    11. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    17. 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.
    18. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    19. 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.
    20. 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.
    21. 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.
    22. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
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    24. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
    25. Pradeep Dubey, 1982. "The Shapley Value as Aircraft Landing Fees--Revisited," Management Science, INFORMS, vol. 28(8), pages 869-874, August.
    26. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    27. Stefano Moretti & Fioravante Patrone, 2004. "Cost allocation games with information costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 419-434, July.
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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. 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.
    5. Algaba, Encarnación & Béal, Sylvain & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Relationship between labeled network games and other cooperative games arising from attributes situations," Economics Letters, Elsevier, vol. 185(C).
    6. Giulia Bernardi & Roberto Lucchetti, 2015. "Generating Semivalues via Unanimity Games," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1051-1062, September.
    7. 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.
    8. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    9. Tom C. van der Zanden & Hans L. Bodlaender & Herbert J. M. Hamers, 2023. "Efficiently computing the Shapley value of connectivity games in low-treewidth graphs," Operational Research, Springer, vol. 23(1), pages 1-23, March.
    10. 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.
    11. 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.
    12. José M. Alonso-Meijide & Julián Costa & Ignacio García-Jurado, 2019. "Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1027-1035, March.
    13. 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.
    14. 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.
    15. Voswinkel, Simon & Höckner, Jonas & Khalid, Abuzar & Weber, Christoph, 2022. "Sharing congestion management costs among system operators using the Shapley value," Applied Energy, Elsevier, vol. 317(C).
    16. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2023. "Efficient effort equilibrium in cooperation with pairwise cost reduction," Omega, Elsevier, vol. 121(C).
    17. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2020. "On egalitarian values for cooperative games with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 672-688, October.
    18. 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.
    19. 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, vol. 7(3), pages 1-23, July.
    20. 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.
    21. 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.
    22. 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.
    23. Sylvain Béal & Issofa Moyouwou & Eric Rémila & Phillippe Solal, 2018. "Cooperative games on intersection closed systems and the Shapley value," Working Papers 2018-06, CRESE.
    24. Kouladoum, Jean-Claude, 2019. "Décision du mariage des ménages tchadiens et Caractéristiques socio-économiques [Marriage decision of Chadian households and socio-economic characteristics]," MPRA Paper 91590, University Library of Munich, Germany.
    25. Margaretha Gansterer & Richard F. Hartl, 2020. "Shared resources in collaborative vehicle routing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-20, April.

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