Abstract
In 1966, W. Lucas [1] exhibited a 10 person game with no von Neumann-Morgenstern solution. D. Schmeidler [2] then originated the nucleolus, proved it exists for every game, is unique and is contained in the kernel and the bargaining set (thereby establishing the first elementary proof of their existence). Charnes’ idea of defining solutions by use of uni- or poly-extremal principles involving comparison of coalitional worths and payoffs thereto was specialized by Charnes and Kortanek [3] to non-Archimedean linear programs characterizing and generalizing the nucleolus and to the class of convex nucleus solutions given by minimizing a convex function of the coalitional excesses subject to simple conditions like the payoff vector being a division of the grand coalition value or an imputation.
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References
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© 1988 Martinus Nijhoff Publishers, Dordrecht
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Charnes, A., Golany, B., Keane, M., Rousseau, J. (1988). Extremal Principle Solutions of Games in Characteristic Function Form: Core, Chebychev and Shapley Value Generalizations. In: Sengupta, J.K., Kadekodi, G.K. (eds) Econometrics of Planning and Efficiency. Advanced Studies in Theoretical and Applied Econometrics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3677-5_7
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DOI: https://doi.org/10.1007/978-94-009-3677-5_7
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