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An average lexicographic value for cooperative games

  • Tijs, Stef
  • Borm, Peter
  • Lohmann, Edwin
  • Quant, Marieke

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.

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

Volume (Year): 213 (2011)
Issue (Month): 1 (August)
Pages: 210-220

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Handle: RePEc:eee:ejores:v:213:y:2011:i:1:p:210-220
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  2. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
  3. Quant, Marieke & Borm, Peter & Hendrickx, Ruud & Zwikker, Peter, 2006. "Compromise solutions based on bankruptcy," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 247-256, May.
  4. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  5. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & van Velzen, S., 2005. "The core cover in relation to the nucleolus and the Weber set," Other publications TiSEM 9723cee6-92c9-49a2-90d3-9, Tilburg University, School of Economics and Management.
  6. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Discussion Paper 2008-8, Tilburg University, Center for Economic Research.
  7. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer, vol. 32(2), pages 189-204, December.
  8. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
  9. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  10. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  11. Reijnierse, J.H. & Maschler, M.B. & Potters, J.A.M. & Tijs, S.H., 1996. "Simple flow games," Other publications TiSEM 1627a9be-de9d-4905-b68a-1, Tilburg University, School of Economics and Management.
  12. Brânzei, R. & Tijs, S.H., 2001. "Additivity Regions for Solutions in Cooperative Game Theory," Discussion Paper 2001-81, Tilburg University, Center for Economic Research.
  13. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
  14. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  15. Reijnierse, Hans & Maschler, Michael & Potters, Jos & Tijs, Stef, 1996. "Simple Flow Games," Games and Economic Behavior, Elsevier, vol. 16(2), pages 238-260, October.
  16. Lohmann, E.R.M.A. & Borm, P.E.M. & Quant, M., 2007. "A Stroll with Alexia," Discussion Paper 2007-52, Tilburg University, Center for Economic Research.
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