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Matrix-vector representation of various solution concepts

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  • Fuad Aleskerov
  • Andrey Subochev

Abstract

A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose several new versions of solution sets.

Suggested Citation

  • Fuad Aleskerov & Andrey Subochev, 2016. "Matrix-vector representation of various solution concepts," Papers 1607.02378, arXiv.org.
    • Handle: RePEc:arx:papers:1607.02378
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    File URL: http://arxiv.org/pdf/1607.02378
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    References listed on IDEAS

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    1. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 491-506, April.
    2. Schwartz, Thomas, 1977. "Collective Choice, Separation of Issues and Vote Trading," American Political Science Review, Cambridge University Press, vol. 71(3), pages 999-1010, September.
    3. Subochev, Andrey, 2008. "Dominant, weakly stable, uncovered sets: properties and extensions," MPRA Paper 53421, University Library of Munich, Germany.
    4. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    5. Deb, Rajat, 1977. "On Schwartz's rule," Journal of Economic Theory, Elsevier, vol. 16(1), pages 103-110, October.
    6. Benjamin Ward, 1961. "Majority rule and allocation," Journal of Conflict Resolution, Peace Science Society (International), vol. 5(4), pages 379-389, December.
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    Cited by:

    1. Subochev, Andrey & Zakhlebin, Igor, 2014. "Alternative versions of the global competitive industrial performance ranking constructed by methods from social choice theory," MPRA Paper 67462, University Library of Munich, Germany.
    2. Fuad T. Aleskerov & Vladimir V. Pislyakov & Andrey N. Subochev, 2014. "Ranking Journals In Economics, Management And Political Science By Social Choice Theory Methods," HSE Working papers WP BRP 27/STI/2014, National Research University Higher School of Economics.
    3. Fuad Aleskerov & Sergey Shvydun, 2019. "Allocation of Disputable Zones in the Arctic Region," Group Decision and Negotiation, Springer, vol. 28(1), pages 11-42, February.

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