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A Bankruptcy Approach to the Core Cover

Author

Listed:
  • Arantza Estévez-Fernández

    (VU University Amsterdam)

  • María Gloria Fiestras-Janeiro

    (Vigo University)

  • Manuel Alfredo Mosquera

    (Vigo University)

  • Estela Sánchez- Rodríguez

    (Vigo University)

Abstract

In this paper we establish a relationship between the core cover of a compromise admissiblegame and the core of a particular bankruptcy game: the core cover of a compromiseadmissible game is, indeed, a translation of the set of coalitional stable allocations capturedby an associated bankruptcy game. Moreover, we analyze the combinatorial complexity ofthe core cover and, consequently, of the core of a compromise stable game.

Suggested Citation

  • Arantza Estévez-Fernández & María Gloria Fiestras-Janeiro & Manuel Alfredo Mosquera & Estela Sánchez- Rodríguez, 2012. "A Bankruptcy Approach to the Core Cover," Tinbergen Institute Discussion Papers 12-012/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20120012
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    References listed on IDEAS

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    1. Julio Díaz & Peter Borm & Ruud Hendrickx & Marieke Quant, 2005. "A geometric characterisation of the compromise value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 483-500, July.
    2. Platz, T.T. & Hamers, H.J.M. & Quant, M., 2011. "Characterizing Compromise Stability of Games Using Larginal Vectors," Other publications TiSEM f6ed49a9-4a91-4db3-ba9a-c, 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. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    5. 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.
    6. 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.
    7. 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.
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    Citations

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    Cited by:

    1. Trine Platz & Herbert Hamers & Marieke Quant, 2014. "C-complete sets for compromise stable games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 213-223, October.
    2. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    3. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2020. "The boundary of the core of a balanced game: face games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 579-599, June.

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    More about this item

    Keywords

    Cooperative game theory; compromise admissible games; bankruptcy; core cover; complexity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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