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Core Solutions in Vector-Valued Games

Author

Listed:
  • F. R. Fernández

    (Universidad de Sevilla)

  • M. A. Hinojosa

    (Universidad Pablo de Olavide)

  • J. Puerto

    (Universidad de Sevilla)

Abstract

In this paper, we analyze core solution concepts for vector-valued cooperative games. In these games, the worth of a coalition is given by a vector rather than by a scalar. Thus, the classical concepts in cooperative game theory have to be revisited and redefined; the important principles of individual and collective rationality must be accommodated; moreover, the sense given to the domination relationship gives rise to two different theories. Although different, we show the areas which they share. This analysis permits us to propose a common solution concept that is analogous to the core for scalar cooperative games.

Suggested Citation

  • F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:2:d:10.1023_a:1013606007132
    DOI: 10.1023/A:1013606007132
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    References listed on IDEAS

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    1. F.R. Fernández & J. Puerto & L. Monroy, 1998. "Two-person non-zero-sum gamesas multicriteria goal games," Annals of Operations Research, Springer, vol. 84(0), pages 195-208, December.
    2. Carrizosa, E. & Conde, E. & Fernandez, F. R. & Puerto, J., 1995. "Multi-criteria analysis with partial information about the weighting coefficients," European Journal of Operational Research, Elsevier, vol. 81(2), pages 291-301, March.
    3. F. R. Fernández & L. Monroy & J. Puerto, 1998. "Multicriteria Goal Games," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 403-421, November.
    4. Ralph E. Steuer, 1976. "Multiple Objective Linear Programming with Interval Criterion Weights," Management Science, INFORMS, vol. 23(3), pages 305-316, November.
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    Cited by:

    1. D. V. Borrero & M. A. Hinojosa & A. M. Mármol, 2016. "Stable solutions for multiple scenario cost allocation games with partial information," Annals of Operations Research, Springer, vol. 245(1), pages 209-226, October.
    2. Bossert, Walter & Derks, Jean & Peters, Hans, 2005. "Efficiency in uncertain cooperative games," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 12-23, July.
    3. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    4. Hinojosa, M. A. & Marmol, A. M. & Thomas, L. C., 2005. "Core, least core and nucleolus for multiple scenario cooperative games," European Journal of Operational Research, Elsevier, vol. 164(1), pages 225-238, July.
    5. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2010. "The truncated core for games with upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 645-656, October.
    6. Monroy, Luisa & Fernández, Francisco R., 2011. "The Shapley-Shubik index for multi-criteria simple games," European Journal of Operational Research, Elsevier, vol. 209(2), pages 122-128, March.
    7. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2015. "Set-valued DEA production games," Omega, Elsevier, vol. 52(C), pages 92-100.
    8. R. Branzei & O. Branzei & S. Alparslan Gök & S. Tijs, 2010. "Cooperative interval games: a survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 397-411, September.
    9. Kuzyutin, Denis & Smirnova, Nadezhda & Gromova, Ekaterina, 2019. "Long-term implementation of the cooperative solution in a multistage multicriteria game," Operations Research Perspectives, Elsevier, vol. 6(C).
    10. Alparslan Gök, S.Z. & Branzei, O. & Branzei, R. & Tijs, S., 2011. "Set-valued solution concepts using interval-type payoffs for interval games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 621-626.
    11. M.A. Hinojosa & A.M. Mármol & L.C. Thomas, 2005. "A multi‐objective model for bank ATM networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(2), pages 165-177, March.
    12. Gayer, Gabrielle & Persitz, Dotan, 2016. "Negotiation across multiple issues," Theoretical Economics, Econometric Society, vol. 11(3), September.
    13. Luis A. Guardiola & Ana Meca & Justo Puerto, 2021. "Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging," Mathematics, MDPI, vol. 9(8), pages 1-19, April.
    14. Luisa Monroy & Francisco Fernández, 2012. "Stable sets and cores for multi-criteria simple games and for their extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 1-22, June.

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