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Minimal stable sets in tournaments

  • Brandt, Felix
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    We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000706
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    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 146 (2011)
    Issue (Month): 4 (July)
    Pages: 1481-1499

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    Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1481-1499
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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    1. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
    2. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    3. Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer, vol. 20(3), pages 523-528, 06.
    4. Bordes, Georges, 1976. "Consistency, Rationality and Collective Choice," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 451-57, October.
    5. Felix Brandt & Felix Fischer & Paul Harrenstein & Maximilian Mair, 2010. "A computational analysis of the tournament equilibrium set," Social Choice and Welfare, Springer, vol. 34(4), pages 597-609, April.
    6. Bordes, Georges, 1983. "On the possibility of reasonable consistent majoritarian choice: Some positive results," Journal of Economic Theory, Elsevier, vol. 31(1), pages 122-132, October.
    7. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, June.
    8. Wilson, Robert B., 1970. "The finer structure of revealed preference," Journal of Economic Theory, Elsevier, vol. 2(4), pages 348-353, December.
    9. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    10. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    11. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    12. Felix Brandt & Paul Harrenstein, 2010. "Characterization of dominance relations in finite coalitional games," Theory and Decision, Springer, vol. 69(2), pages 233-256, August.
    13. Nicolas Houy, 2009. "Still more on the Tournament Equilibrium Set," Social Choice and Welfare, Springer, vol. 32(1), pages 93-99, January.
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