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Convex multi-choice games: Characterizations and monotonic allocation schemes

  • Branzei, R.
  • Tijs, S.
  • Zarzuelo, J.

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Furthermore, level-increase monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is extendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.

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

Volume (Year): 198 (2009)
Issue (Month): 2 (October)
Pages: 571-575

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Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:571-575
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  1. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the Shapley value: a new approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00178916, HAL.
  2. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Discussion Paper 2007-55, Tilburg University, Center for Economic Research.
  3. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-66.
  4. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "Egalitarianism in convex fuzzy games," Other publications TiSEM feab7e25-2f43-47e3-9658-b, Tilburg University, School of Economics and Management.
  5. repec:hal:journl:halshs-00178916 is not listed on IDEAS
  6. repec:spr:compst:v:66:y:2007:i:3:p:491-512 is not listed on IDEAS
  7. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "A New Characterization of Convex Games," Discussion Paper 2004-109, Tilburg University, Center for Economic Research.
  8. repec:spr:compst:v:65:y:2007:i:1:p:153-167 is not listed on IDEAS
  9. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
  10. repec:hal:journl:halshs-00267933 is not listed on IDEAS
  11. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  12. Michel Grabisch & Lijue Xie, 2007. "A new approach to the core and Weber set of multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 491-512, December.
  13. Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 327-338.
  14. José Zarzuelo & Marco Slikker & Flip Klijn, 1999. "Characterizations of a multi-choice value," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 521-532.
  15. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  16. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  17. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
  18. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  19. Esther GutiÊrrez & Emilio Calvo & Juan Carlos Santos, 2000. "The multichoice consistent value," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 177-188.
  20. Hans Peters & Horst Zank, 2005. "The Egalitarian Solution for Multichoice Games," Annals of Operations Research, Springer, vol. 137(1), pages 399-409, July.
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