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An Axiomatization of the Banzhaf Value

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Cited by:

  1. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 309-319.
  2. Sven Berg, 1999. "On Voting Power Indices and a Class of Probability Distributions: With applications to EU data," Group Decision and Negotiation, Springer, vol. 8(1), pages 17-31, January.
  3. Robert P. Gilles & Lina Mallozzi, 2022. "Gately Values of Cooperative Games," Papers 2208.10189, arXiv.org, revised Jul 2023.
  4. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring Power and Satisfaction in Societies with Opinion Leaders," PSE-Ecole d'économie de Paris (Postprint) hal-00756720, HAL.
  5. van den Brink, J.R. & van der Laan, G., 1999. "Potentials and Reduced Games for Share Functions," Other publications TiSEM bb166cb9-4f1c-4e52-b4b9-0, Tilburg University, School of Economics and Management.
  6. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "A strategic implementation of the sequential equal surplus division rule for digraph cooperative games," Annals of Operations Research, Springer, vol. 253(1), pages 43-59, June.
  7. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
  8. Oriol Tejada & Mikel Álvarez-Mozos, 2017. "Games with Graph Restricted Communication and Levels Structure of Cooperation," UB School of Economics Working Papers 2017/363, University of Barcelona School of Economics.
  9. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
  10. van den Brink, Rene & van der Laan, Gerard, 2005. "A class of consistent share functions for games in coalition structure," Games and Economic Behavior, Elsevier, vol. 51(1), pages 193-212, April.
  11. Berghammer, Rudolf & Bolus, Stefan & Rusinowska, Agnieszka & de Swart, Harrie, 2011. "A relation-algebraic approach to simple games," European Journal of Operational Research, Elsevier, vol. 210(1), pages 68-80, April.
  12. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
  13. Nicola G. Andjiga & Sebastien Courtin, 2013. "Coalition configurations and share functions," Working Papers hal-00914883, HAL.
  14. Nicolas Andjiga & Sebastien Courtin, 2015. "Coalition configurations and share functions," Annals of Operations Research, Springer, vol. 225(1), pages 3-25, February.
  15. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
  16. Ori Haimanko, 2019. "Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 755-768, September.
  17. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
  18. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August.
  19. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
  20. Bendel, Dan & Haviv, Moshe, 2018. "Cooperation and sharing costs in a tandem queueing network," European Journal of Operational Research, Elsevier, vol. 271(3), pages 926-933.
  21. Ori Haimanko, 2020. "Generalized Coleman-Shapley indices and total-power monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 299-320, March.
  22. van den Brink, René, 2012. "Efficiency and collusion neutrality in cooperative games and networks," Games and Economic Behavior, Elsevier, vol. 76(1), pages 344-348.
  23. Francesc Carreras, 2009. "Protectionism and blocking power indices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 70-84, July.
  24. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Post-Print halshs-02381119, HAL.
  25. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
  26. Atteya, T.E.M. & Chakhar, Salem & Labib, Ashraf & Cox, Adam & Ishizaka, Alessio, 2024. "Estimating relative importance of criteria by post-processing dominance-based rough set approach’s outputs," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1096-1122.
  27. Tadeusz Radzik & Andrzej Nowak & Theo Driessen, 1997. "Weighted Banzhaf values," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 109-118, February.
  28. Haimanko, Ori, 2018. "The axiom of equivalence to individual power and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 108(C), pages 391-400.
  29. Duygu Yengin, 2012. "Characterizing the Shapley value in fixed-route traveling salesman problems with appointments," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 271-299, May.
  30. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
  31. En-Cheng Chi & Yu-Hsien Liao, 2021. "Sustainable Usability Distribution Mechanisms under Multi-Attribute Sports Management Schemes," Sustainability, MDPI, vol. 13(3), pages 1-16, February.
  32. André Casajus, 2014. "Collusion, quarrel, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 1-11, February.
  33. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
  34. Pérez-Castrillo, David & Sun, Chaoran, 2021. "Value-free reductions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 543-568.
  35. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 445-466, July.
  36. 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.
  37. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
  38. 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.
  39. Gerard van der Laan & René van den Brink, 2001. "Core concepts for share vectors," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 759-784.
  40. Fabien Lange & László Kóczy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 281-292, July.
  41. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2012. "The Sequential Equal Surplus Division for Sharing International Rivers with Bifurcations," Working Papers 2012-02, CRESE.
  42. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
  43. Carreras, Francesc & Freixas, Josep & Puente, Maria Albina, 2003. "Semivalues as power indices," European Journal of Operational Research, Elsevier, vol. 149(3), pages 676-687, September.
  44. Rene van den Brink & Chris Dietz, 2012. "Multi-Player Agents in Cooperative TU-Games," Tinbergen Institute Discussion Papers 12-001/1, Tinbergen Institute.
  45. Tejada, O. & Álvarez-Mozos, M., 2018. "Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 114-122.
  46. J. Alonso-Meijide & B. Casas-Méndez & A. González-Rueda & S. Lorenzo-Freire, 2014. "Axiomatic of the Shapley value of a game 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. 22(2), pages 749-770, July.
  47. Trine Tornøe Platz & Lars Peter Østerdal, 2013. "Forming and Dissolving Partnerships in Cooperative Game Situations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(2), pages 208-228, April.
  48. Courtin, Sébastien, 2022. "Evaluation of decision power in multi-dimensional rules," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 27-36.
  49. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
  50. Barua, Rana & Chakravarty, Satya R. & Sarkar, Palash, 2009. "Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 367-375, November.
  51. Amer, Rafael & Gimenez, Jose Miguel, 2007. "The two-person blocks as a way to emphasize several semivalues," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 172-184, March.
  52. Nicolas G. Andjiga & Sébastien Courtin, 2015. "Coalition configurations and share functions," Post-Print hal-00914883, HAL.
  53. Rahmoune, Mahdi & Radjef, Mohammed Said & Boukherroub, Tasseda & Carvalho, Margarida, 2024. "A new integrated cooperative game and optimization model for the allocation of forest resources," European Journal of Operational Research, Elsevier, vol. 316(1), pages 329-340.
  54. Rene van den Brink, 2009. "Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games," Tinbergen Institute Discussion Papers 09-065/1, Tinbergen Institute.
  55. Artyom Jelnov & Yair Tauman, 2014. "Voting power and proportional representation of voters," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 747-766, November.
  56. Ori Haimanko, 2019. "The Banzhaf Value and General Semivalues for Differentiable Mixed Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 767-782, August.
  57. Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
  58. van den Brink, J.R., 1999. "An Axiomatization of the Shapley Value Using a Fairness Property," Other publications TiSEM 0090365c-9bab-4367-b660-5, Tilburg University, School of Economics and Management.
  59. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarkar, Palash, 2004. "A characterization and some properties of the Banzhaf-Coleman-Dubey-Shapley sensitivity index," Games and Economic Behavior, Elsevier, vol. 49(1), pages 31-48, October.
  60. Haviv, Moshe, 1995. "Consecutive amalgamations and an axiomatization of the Shapley value," Economics Letters, Elsevier, vol. 49(1), pages 7-11, July.
  61. Yu-Hsien Liao, 2023. "Power Indices under Specific Multicriteria Status," Games, MDPI, vol. 14(4), pages 1-10, June.
  62. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali, 2006. "On the Coleman indices of voting power," European Journal of Operational Research, Elsevier, vol. 171(1), pages 273-289, May.
  63. repec:hal:pseose:hal-00756720 is not listed on IDEAS
  64. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "Axiomatization of an allocation rule for ordered tree TU-games," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 132-140.
  65. M. Albizuri, 2009. "The multichoice coalition value," Annals of Operations Research, Springer, vol. 172(1), pages 363-374, November.
  66. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
  67. Margarita Domènech & José Miguel Giménez & María Albina Puente, 2022. "Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues," Annals of Operations Research, Springer, vol. 318(2), pages 889-910, November.
  68. Mágó, Mánuel, 2018. "Power values and framing in game theory," Other publications TiSEM e7822a6b-a2db-4ce9-bd08-b, Tilburg University, School of Economics and Management.
  69. Sanchez S., Francisco, 1997. "Balanced Contributions Axiom in the Solution of Cooperative Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 161-168, August.
  70. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "The sequential equal surplus division for sharing a river," MPRA Paper 37346, University Library of Munich, Germany.
  71. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
  72. Amer, Rafael & Gimenez, Jose Miguel, 2006. "An axiomatic characterization for regular semivalues," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 217-226, March.
  73. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
  74. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
  75. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
  76. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
  77. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
  78. Sylvain Béal & Eric Rémila & Philippe Solal, 2014. "Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value," Working Papers 2014-05, CRESE.
  79. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
  80. Ramón Flores & Elisenda Molina & Juan Tejada, 2019. "Evaluating groups with the generalized Shapley value," 4OR, Springer, vol. 17(2), pages 141-172, June.
  81. McQuillin, Ben & Sugden, Robert, 2018. "Balanced externalities and the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 81-92.
  82. Satoshi Masuya, 2023. "Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games," Mathematics, MDPI, vol. 12(1), pages 1-15, December.
  83. Chunqiao Tan & Wenrui Feng & Weibin Han, 2020. "On the Banzhaf-like Value for Cooperative Games with Interval Payoffs," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
  84. Pradeep Dubey & Ezra Einy & Ori Haimanko, 2003. "Compound Voting and the Banzhaf Power Index," Discussion Paper Series dp333, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  85. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 679-694, April.
  86. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
  87. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 571-596, June.
  88. Arash Abizadeh & Adrian Vetta, 2023. "The blocker postulates for measures of voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 595-623, May.
  89. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
  90. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.
  91. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
  92. Giulia Bernardi, 2018. "A New Axiomatization of the Banzhaf Index for Games with Abstention," Group Decision and Negotiation, Springer, vol. 27(1), pages 165-177, February.
  93. André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 497-515, August.
  94. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.
  95. Besner, Manfred, 2018. "Player splitting, players merging, the Shapley set value and the Harsanyi set value," MPRA Paper 87125, University Library of Munich, Germany.
  96. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.
  97. Rafael Amer & José Miguel Giménez, 2007. "Technical note: Characterization of binomial semivalues through delegation games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 702-708, September.
  98. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 47-67.
  99. Francesc Carreras & María Albina Puente, 2012. "Symmetric Coalitional Binomial Semivalues," Group Decision and Negotiation, Springer, vol. 21(5), pages 637-662, September.
  100. Gilles, Robert P. & Mallozzi, Lina, 2022. "Generalised Gately Values of Cooperative Games," QBS Working Paper Series 2022/06, Queen's University Belfast, Queen's Business School.
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