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Shadow Prices for Measures of Effectiveness, II: General Model

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  • Stephen M. Robinson

    (University of Wisconsin, Madison, Wisconsin)

Abstract

This is the second of a pair of papers describing a two-sided game model of combat. In this paper, each side attempts to develop a force structure attaining the maximum of a prescribed merit function, subject to certain constraints expressed by a set of prescribed measures of effectiveness. These measures can be different for the two sides: furthermore, those of each side can depend on the other side's actions. A solution of the model is a generalized Nash equilibrium of this game, and such a solution also yields shadow prices that reveal the cost in merit paid by each side for requiring the specified level of performance on each measure of effectiveness. The first paper examines a special case in which the model has a linear structure, and shows that in a restricted case the shadow prices produced by that model are the classical eigenvalue weights familiar from Lanchester theory.

Suggested Citation

  • Stephen M. Robinson, 1993. "Shadow Prices for Measures of Effectiveness, II: General Model," Operations Research, INFORMS, vol. 41(3), pages 536-548, June.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:3:p:536-548
    DOI: 10.1287/opre.41.3.536
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    Cited by:

    1. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    2. Masao Fukushima, 2011. "Restricted generalized Nash equilibria and controlled penalty algorithm," Computational Management Science, Springer, vol. 8(3), pages 201-218, August.
    3. Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.
    4. Jianzhong Zhang & Biao Qu & Naihua Xiu, 2010. "Some projection-like methods for the generalized Nash equilibria," Computational Optimization and Applications, Springer, vol. 45(1), pages 89-109, January.
    5. Rodrick Wallace, 2024. "“Neuroscience†models of institutional conflict under fog, friction, and adversarial intent," The Journal of Defense Modeling and Simulation, , vol. 21(1), pages 75-86, January.
    6. Lowell Bruce Anderson & Frederic A. Miercort, 1995. "On weapons scores and force strengths," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(3), pages 375-395, April.
    7. Koichi Nabetani & Paul Tseng & Masao Fukushima, 2011. "Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints," Computational Optimization and Applications, Springer, vol. 48(3), pages 423-452, April.
    8. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    9. Krawczyk, Jacek B., 2005. "Coupled constraint Nash equilibria in environmental games," Resource and Energy Economics, Elsevier, vol. 27(2), pages 157-181, June.
    10. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.

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