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A Simple Expression for the Shapley Value in a Special Case

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Cited by:

  1. Dan C. Popescu & Philip Kilby, 2020. "Approximation of the Shapley value for the Euclidean travelling salesman game," Annals of Operations Research, Springer, vol. 289(2), pages 341-362, June.
  2. Vásquez-Brage, M. & van den Nouweland, C.G.A.M. & García-Jurado, I., 1995. "Owen's coalitional value and aircraft landing fees," Discussion Paper 1995-104, Tilburg University, Center for Economic Research.
  3. Cristina Fernández & Peter Borm & Ruud Hendrickx & Stef Tijs, 2005. "Drop out monotonic rules for sequencing situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 501-504, July.
  4. Fragnelli, Vito & Gagliardo, Stefano, 2012. "Cooperative models for allocating an object," Economics Letters, Elsevier, vol. 117(1), pages 227-229.
  5. Dehez, Pierre, 2021. "1-convex transferable utility games, a reappraisal," LIDAM Discussion Papers CORE 2021016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. René Brink, 2012. "On hierarchies and communication," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 721-735, October.
  7. José Alcalde & Matthias Dahm, 2007. "Tullock and Hirshleifer: a meeting of the minds," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 101-124, September.
  8. Forges, Françoise & Orzach, Ram, 2011. "Core-stable rings in second price auctions with common values," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 760-767.
  9. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
  10. Yan-An Hwang & Chun-Hsien Yeh, 2012. "A characterization of the nucleolus without homogeneity in airport problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 355-364, February.
  11. Norde, Henk & Fragnelli, Vito & Garcia-Jurado, Ignacio & Patrone, Fioravante & Tijs, Stef, 2002. "Balancedness of infrastructure cost games," European Journal of Operational Research, Elsevier, vol. 136(3), pages 635-654, February.
  12. Martin Shubik, 1984. "The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits," Cowles Foundation Discussion Papers 706, Cowles Foundation for Research in Economics, Yale University.
  13. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  14. Sylvain Béal & Marc Deschamps & Catherine Refait-Alexandre & Guillaume Sekli, 2022. "Early contributors, cooperation and fair rewards in crowdfunding," Working Papers hal-04222321, HAL.
  15. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
  16. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
  17. Algaba, Encarnación & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Horizontal cooperation in a multimodal public transport system: The profit allocation problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 659-665.
  18. R. Brânzei & E. Iñarra & S. Tijs & J. M. Zarzuelo, 2005. "Cooperation by Asymmetric Agents in a Joint Project," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(4), pages 623-640, October.
  19. José Alcalde & José Angel Silva, 2000. "- A Procedure For Sharing Recycling Costs," Working Papers. Serie AD 2000-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  20. Arin Aguirre, Francisco Javier & Iñarra García, María Elena & Luquin, Paloma, 2006. "A noncooperative view on two consistent aiport cost sharing rules," IKERLANAK 2006-23, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  21. Brânzei, R. & Inarra, E. & Tijs, S.H. & Zarzuelo, J., 2003. "An Algorithm for the Nucleolus of Airport Profit Problems," Discussion Paper 2003-50, Tilburg University, Center for Economic Research.
  22. António Osório, 2017. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Group Decision and Negotiation, Springer, vol. 26(2), pages 357-377, March.
  23. 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.
  24. Flip Klijn & Stef Tijs & Marco Slikker, 2001. "A Dual Egalitarian Solution," Economics Bulletin, AccessEcon, vol. 3(10), pages 1-8.
  25. Takayuki Oishi & Shin Sakaue, 2014. "A Microeconomic Analysis toward Building Liability Lawin the Post-Earthquake Era," KIER Working Papers 890, Kyoto University, Institute of Economic Research.
  26. Hougaard, Jens Leth & Tvede, Mich & Østerdal, Lars Peter, 2013. "Cost Sharing in Chains and Other Fixed Trees," Discussion Papers on Economics 12/2013, University of Southern Denmark, Department of Economics.
  27. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
  28. Louis de Mesnard, 2015. "The three wives problem and Shapley value," Post-Print hal-01091714, HAL.
  29. M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
  30. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2012. "Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 185-197.
  31. Sonmez, Tayfun O., 2014. "Population-Monotonicity of the Nucleolus on a Class of Public Good Problems," MPRA Paper 58248, University Library of Munich, Germany.
  32. Vásquez-Brage, M. & van den Nouweland, C.G.A.M. & García-Jurado, I., 1995. "Owen's coalitional value and aircraft landing fees," Other publications TiSEM 3f2bc27b-b5c8-4517-8ffd-8, Tilburg University, School of Economics and Management.
  33. René van den Brink, 2009. "Comparable Axiomatizations of the Myerson Value, the Restricted Banzhaf Value, Hierarchical Outcomes and the Average Tree Solution for Cycle-Free Graph Restricted Games," Tinbergen Institute Discussion Papers 09-108/1, Tinbergen Institute.
  34. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
  35. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Other publications TiSEM ef12f1e8-87f5-41b4-97e4-7, Tilburg University, School of Economics and Management.
  36. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
  37. Voorneveld, M. & Grahn, S., 2001. "A Minimal Test for Convex Games and the Shapley Value," Papers 2001:02, Uppsala - Working Paper Series.
  38. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
  39. Shoshana Anily, 2018. "Full characterization of the nonnegative core of some cooperative games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 303-316, June.
  40. Alcalde-Unzu, Jorge & Moreno-Ternero, Juan D. & Weber, Shlomo, 2022. "The measurement of the value of a language," Journal of Economic Theory, Elsevier, vol. 203(C).
  41. Youngsub Chun & Boram Park, 2012. "Population solidarity, population fair-ranking, and the egalitarian value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 255-270, May.
  42. Habis, Helga & Herings, P. Jean-Jacques, 2011. "Transferable utility games with uncertainty," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2126-2139, September.
  43. Van Essen, Matt & Wooders, John, 2021. "Allocating positions fairly: Auctions and Shapley value," Journal of Economic Theory, Elsevier, vol. 196(C).
  44. Juan Aparicio & Joaquín Sánchez-Soriano, 2008. "Depreciation games," Annals of Operations Research, Springer, vol. 158(1), pages 205-218, February.
  45. Rodica Brânzei & Elena Iñarra & Stef Tijs & José Zarzuelo, 2006. "A Simple Algorithm for the Nucleolus of Airport Profit Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 259-272, August.
  46. Hiroki Baba & Yasushi Asami, 2020. "Estimating the minimal efficient scale and the effect of intermunicipal cooperation on service provision areas for waste treatment in Japan," Asia-Pacific Journal of Regional Science, Springer, vol. 4(1), pages 139-158, February.
  47. Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
  48. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2022. "Optimal Management of Evolving Hierarchies," Management Science, INFORMS, vol. 68(8), pages 6024-6038, August.
  49. van Riel, A.C.R. & Semeijn, J. & Pauwels, P.F.J., 2003. "Online travel service quality: the importance of pre-transaction services," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  50. 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.
  51. Ata Atay & Christian Trudeau, 2024. "Optimistic and pessimistic approaches for cooperative games," Working Papers 2401, University of Windsor, Department of Economics.
  52. Dehez, Pierre, 2023. "Sharing a collective probability of success," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 122-127.
  53. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
  54. Yuji Fujinaka & Toyotaka Sakai, 2009. "The positive consequence of strategic manipulation in indivisible good allocation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 325-348, November.
  55. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
  56. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2016. "Monotonicity implications for the ranking of rules for airport problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 379-400, December.
  57. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
  58. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
  59. Youngsub Chun & Boram Park, 2016. "The airport problem with capacity constraints," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 237-253, September.
  60. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
  61. de Clippel, Geoffroy & Bejan, Camelia, 2011. "No profitable decompositions in quasi-linear allocation problems," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1995-2012, September.
  62. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Other publications TiSEM ad3fc093-38be-4802-aa35-a, Tilburg University, School of Economics and Management.
  63. Jeroen Kuipers & Dries Vermeulen & Mark Voorneveld, 2010. "A generalization of the Shapley–Ichiishi result," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 585-602, October.
  64. Minyoung Yea & Seokhyun Chung & Taesu Cheong & Daeki Kim, 2018. "The Sharing of Benefits from a Logistics Alliance Based on a Hub-Spoke Network: A Cooperative Game Theoretic Approach," Sustainability, MDPI, vol. 10(6), pages 1-16, June.
  65. Sanchez-Soriano, Joaquin, 2003. "The pairwise egalitarian solution," European Journal of Operational Research, Elsevier, vol. 150(1), pages 220-231, October.
  66. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cooperative Interval Games Arising from Airport Situations with Interval Data," Other publications TiSEM 5ded50b5-2a11-4d25-8511-b, Tilburg University, School of Economics and Management.
  67. Baomin Dong & Debing Ni & Yuntong Wang, 2012. "Sharing a Polluted River Network," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(3), pages 367-387, November.
  68. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
  69. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
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  71. Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2010. "Sharing the Cost of a Capacity Network," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 173-192, February.
  72. Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
  73. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
  74. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
  75. Mikel Álvarez-Mozos & René van den Brink & Gerard van der Laan & Oriol Tejada, 2015. "From Hierarchies to Levels: New Solutions for Games," Tinbergen Institute Discussion Papers 15-072/II, Tinbergen Institute.
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  77. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "Manipulability in the cost allocation of transport systems," ThE Papers 20/08, Department of Economic Theory and Economic History of the University of Granada..
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  80. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
  81. Matt Van Essen & John Wooders, 2018. "Allocating Positions Fairly: An Auction and its Relationship to the Shapley Value," Working Papers 20180019, New York University Abu Dhabi, Department of Social Science, revised Aug 2018.
  82. Habis, Helga, 2012. "Sztochasztikus csődjátékok - avagy hogyan osszunk szét egy bizonytalan méretű tortát? [Stochastic bankruptcy games. How can a cake of uncertain dimensions be divided?]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1299-1310.
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  84. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
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  119. Balbina Casas-Mendez & Vito Fragnelli & Ignacio Garcìa-Jurado, 2014. "A survey of allocation rules for the museum pass problem," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 38(2), pages 191-205, May.
  120. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2020. "Sharing the Revenues from Broadcasting Sport Events," Management Science, INFORMS, vol. 66(6), pages 2417-2431, June.
  121. Danny Ben-Shahar & Yongheng Deng & Eyal Sulganik, 2006. "Shapley Cost Allocation Coincides with Relative Status: The Case of Skyscrapers," Working Paper 8567, USC Lusk Center for Real Estate.
  122. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
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  124. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On how to allocate the fixed cost of transport systems," Annals of Operations Research, Springer, vol. 301(1), pages 81-105, June.
  125. Lipschütz Itay & Schwarz Mordechai E., 2020. "Fairness Vs. Economic Efficiency: Lessons from an Interdisciplinary Analysis of Talmudic Bankruptcy Law," Review of Law & Economics, De Gruyter, vol. 16(3), pages 1-38, November.
  126. Bergantiños, Gustavo & Groba, Carlos & Sartal, Antonio, 2023. "Applying the Shapley value to the tuna fishery," European Journal of Operational Research, Elsevier, vol. 309(1), pages 306-318.
  127. René Brink & Gerard Laan & Valeri Vasil’ev, 2014. "Constrained core solutions for totally positive games with ordered players," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 351-368, May.
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