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Universal Characterization Sets for the Nucleolus in Balanced Games

Listed author(s):
  • Tamas Solymosi

    ()

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Balazs Sziklai

    ()

    (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

We provide a new modus operandi for the computation of the nucleolus in cooperative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and dually saturated coalitions determine both the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two sets are related with the existing characterization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself. We conclude with a sample computation of the nucleolus of bankruptcy games - the shortest of its kind.

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Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1512.

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Length: 29 pages
Date of creation: Feb 2015
Handle: RePEc:has:discpr:1512
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  1. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
  2. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, 09.
  3. D. Granot & F. Granot & W. R. Zhu, 1998. "Characterization sets for the nucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 359-374.
  4. Groote Schaarsberg, M. & Borm, P.E.M. & Hamers, H.J.M. & Reijnierse, J.H., 2012. "Interactive Purchasing Situations," Discussion Paper 2012-035, Tilburg University, Center for Economic Research.
  5. Sankaran, Jayaram K, 1991. "On Finding the Nucleolus of an N-Person Cooperative Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 329-338.
  6. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 1998. "Note Computing the nucleolus of min-cost spanning tree games is NP-hard," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 443-450.
  7. Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Other publications TiSEM ab187dab-1b5b-40c3-a673-8, Tilburg University, School of Economics and Management.
  8. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
  9. 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.
  10. Granot, Daniel & Hamers, Herbert & Kuipers, Jeroen & Maschler, Michael, 2011. "On Chinese postman games where residents of each road pay the cost of their road," Games and Economic Behavior, Elsevier, vol. 72(2), pages 427-438, June.
  11. Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 85-106.
  12. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
  13. 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.
  14. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
  15. Michael Maschler & Jos Potters & Hans Reijnierse, 2010. "The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 89-104, March.
  16. Fromen, Bastian, 1997. "Reducing the number of linear programs needed for solving the nucleolus problem of n-person game theory," European Journal of Operational Research, Elsevier, vol. 98(3), pages 626-636, May.
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