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Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value

  • Kamijo, Yoshio
  • Kongo, Takumi

This study provides a unified axiomatic characterization method of one-point solutions for cooperative games with transferable utilities. Any one-point solution that satisfies efficiency, the balanced cycle contributions property (BCC), and the axioms related to invariance under a player deletion is characterized as a corollary of our general result. BCC is a weaker requirement than the well-known balanced contributions property. Any one-point solution that is both symmetric and linear satisfies BCC. The invariance axioms necessitate that the deletion of a specific player from games does not affect the other players’ payoffs, and this deletion is different with respect to solutions. As corollaries of the above characterization result, we are able to characterize the well-known one-point solutions, the Shapley, egalitarian, and solidarity values, in a unified manner. We also studied characterizations of an inefficient one-point solution, the Banzhaf value that is a well-known alternative to the Shapley value.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 216 (2012)
Issue (Month): 3 ()
Pages: 638-646

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Handle: RePEc:eee:ejores:v:216:y:2012:i:3:p:638-646
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  2. Ehud Kalai & Dov Samet, 1983. "Monotonic Solutions to General Cooperative Games," Discussion Papers 567, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer, vol. 26(1), pages 137-141.
  4. Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer, vol. 37(4), pages 533-563, December.
  5. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  6. Arin, J. & Feltkamp, V., 2012. "Coalitional games: Monotonicity and core," European Journal of Operational Research, Elsevier, vol. 216(1), pages 208-213.
  7. repec:dgr:uvatin:20020110 is not listed on IDEAS
  8. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
  9. Feltkamp, V., 1993. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," Papers 9353, Tilburg - Center for Economic Research.
  10. Andrzej S. Nowak & Tadeusz Radzik, 2000. "note: An alternative characterization of the weighted Banzhaf value," International Journal of Game Theory, Springer, vol. 29(1), pages 127-132.
  11. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
  12. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, vol. 23(1), pages 43-48.
  13. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer, vol. 39(3), pages 467-482, July.
  14. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
  15. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
  16. E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2004. "An axiomatization of the Banzhaf value for cooperative games on antimatroids," Mathematical Methods of Operations Research, Springer, vol. 59(1), pages 147-166, 02.
  17. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
  18. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  19. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
  20. Rodica Branzei & Vito Fragnelli & Ana Meca & Stef Tijs, 2009. "On Cooperative Games Related To Market Situations And Auctions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 459-470.
  21. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer, vol. 39(4), pages 563-571, October.
  22. 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.
  23. 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.
  24. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
  25. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  26. repec:spr:compst:v:59:y:2004:i:1:p:147-166 is not listed on IDEAS
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