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Positively homogeneous quasidifferentiable functions and their applications in cooperative game theory

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Quasidifferential Calculus

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 29))

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Abstract

One interesting class of quasidifferentiable functions is that formed by the family of positively homogeneous functions. In this paper, the author studies the properties of these functions and uses them to derive some new results in the theory of cooperative games.

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References

  1. J.-P. Aubin, Mathematical methods of game and economic theory (North-Holland, Amsterdam, 1979).

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  2. J.-P. Aubin, “Cooperative fuzzy games”, Mathematics of Operations Research 6 (1981) 1–13.

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  4. V.F. Demyanov, “On a relation between the Clarke sub-differential and the quasidifferential”, Vestnik Leningradskogo Universiteta 13 (1980) 18–24 (translated in Vestnik Leningrad University Mathematics 13 (1981) 183–189).

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  5. V.F. Demyanov and A.M. Rubinov, “On some approaches to a nonsmooth optimization problem” (in Russian), Ekonomika i Matematicheskie Metody 17 (1981) 1153–1174.

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V. F. Demyanov L. C. W. Dixon

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© 1986 The Mathematical Programming Society, Inc.

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Pechersky, S.L. (1986). Positively homogeneous quasidifferentiable functions and their applications in cooperative game theory. In: Demyanov, V.F., Dixon, L.C.W. (eds) Quasidifferential Calculus. Mathematical Programming Studies, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121143

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  • DOI: https://doi.org/10.1007/BFb0121143

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00928-0

  • Online ISBN: 978-3-642-00929-7

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