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

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  • Yury Nikulin

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. Copyright Springer Science+Business Media, LLC 2009

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  • Yury Nikulin, 2009. "Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies," Annals of Operations Research, Springer, vol. 172(1), pages 25-35, November.
    • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:25-35:10.1007/s10479-008-0471-6
    DOI: 10.1007/s10479-008-0471-6
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    References listed on IDEAS

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    1. Marek Libura & Yury Nikulin, 2006. "Stability and accuracy functions in multicriteria linear combinatorial optimization problems," Annals of Operations Research, Springer, vol. 147(1), pages 255-267, October.
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    Cited by:

    1. Omkar D. Palsule-Desai, 2016. "Impact of equity and equality on stability and collusion in a decentralized network," Annals of Operations Research, Springer, vol. 238(1), pages 411-447, March.
    2. Nikulin, Y. & Karelkina, O. & Mäkelä, M.M., 2013. "On accuracy, robustness and tolerances in vector Boolean optimization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 449-457.
    3. Omkar Palsule-Desai, 2016. "Impact of equity and equality on stability and collusion in a decentralized network," Annals of Operations Research, Springer, vol. 238(1), pages 411-447, March.
    4. Nikulin, Yury & Mäkelä, Marko M., 2010. "Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality "from Condorcet to Pareto"," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1497-1505, December.
    5. Korotkov, Vladimir & Wu, Desheng, 2020. "Evaluating the quality of solutions in project portfolio selection," Omega, Elsevier, vol. 91(C).

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