Shapley-Folkman-Lyapunov Theorem and Asymmetric First Price Auctions

Applied Mathematics and Nonlinear Sciences 4(2) (2019) 331–350

20 Pages Posted: 1 Oct 2019

See all articles by Dushko Josheski

Dushko Josheski

University Goce Delcev

Elena Gelova

University Goce Delcev

Mico Apostolov

University Goce Delcev; University of Turin; Scuola Superiore Sant'Anna di Pisa - School of Social Sciences; University of California, Berkeley - Haas School of Business

Date Written: September 19, 2019

Abstract

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.

Keywords: Shapley-Folkman theorem, asymmetric auctions, Backward shooting method, auction solving, fixed point iterations

JEL Classification: C65, D44

Suggested Citation

Josheski, Dushko and Gelova, Elena and Apostolov, Mico, Shapley-Folkman-Lyapunov Theorem and Asymmetric First Price Auctions (September 19, 2019). Applied Mathematics and Nonlinear Sciences 4(2) (2019) 331–350 , Available at SSRN: https://ssrn.com/abstract=3456539

Dushko Josheski (Contact Author)

University Goce Delcev ( email )

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HOME PAGE: http://www.ugd.edu.mk/

Elena Gelova

University Goce Delcev ( email )

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Macedonia

Mico Apostolov

University Goce Delcev

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Macedonia

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University of Turin ( email )

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Italy
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University of California, Berkeley - Haas School of Business

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