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Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies

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Abstract

A coalition game with a finite number of players in which initial coefficients of linear payoff functions are subject to perturbations is considered. For any efficient solution which may appear in the game, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multiobjective combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied. Maximum norms of perturbations for which an efficient in sense of equilibrium solution preserves the property of being efficient are calculated.

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References

  • Bukhtoyarov, S., Emelichev, V., & Stepanishina, Y. (2006). Stability of discrete vector problems with the parametric principle of optimality. Cybernetics and Systems Analysis, 39, 604–614.

    Article  Google Scholar 

  • Emelichev, V., Girlich, E., Nikulin, Y., & Podkopaev, D. (2002). Stability and regularization of vector problems of integer linear programming. Optimization, 51, 645–676.

    Article  Google Scholar 

  • Ehrgott, M. (2000). Multicriteria optimization. Berlin: Springer.

    Google Scholar 

  • Greenberg, H. (1998). An annotated bibliography for post-solution analysis in mixed integer and combinatorial optimization. In D. Woodruff (Ed.), Advances in computational and stochastic optimization. Logic programming and heuristic search (pp. 97–148).

  • Goldengorin, B., Jäger, G., & Molitor, P. (2006). Tolerances applied in combinatorial optimization. Journal of Computer Science, 2, 716–734.

    Article  Google Scholar 

  • Libura, M. (1999). On accuracy of solution for combinatorial optimization problems with perturbed coefficients of the objective function. Annals of Operation Research, 86, 53–62.

    Article  Google Scholar 

  • Libura, M. (2000). Quality of solutions for perturbed combinatorial optimization problems. Control and Cybernetics, 29, 199–219.

    Google Scholar 

  • Libura, M., & Nikulin, Y. (2004). Stability and accuracy functions in multicriteria combinatorial optimization problem with Σ-MINMAX and Σ-MINMIN partial criteria. Control and Cybernetics, 33, 511–524.

    Google Scholar 

  • Libura, M., & Nikulin, Y. (2006). Stability and accuracy functions in multicriteria linear combinatorial optimization problems. Annals of Operations Research, 147, 255–267.

    Article  Google Scholar 

  • Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 48–49.

    Article  Google Scholar 

  • Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54, 286–295.

    Article  Google Scholar 

  • Pareto, V. (1909). Manuel d’ecoonomie politique. Paris: Qiard.

    Google Scholar 

  • Steuer, R. (1986). Multiple criteria optimization: Theory, computation and application. New York: Wiley.

    Google Scholar 

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  1. Department of Mathematics, University of Turku, Turku, Finland

    Yury Nikulin

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  1. Yury Nikulin
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Correspondence to Yury Nikulin.

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Nikulin, Y. Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies. Ann Oper Res 172, 25–35 (2009). https://doi.org/10.1007/s10479-008-0471-6

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  • DOI: https://doi.org/10.1007/s10479-008-0471-6

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