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
Date Written: September 19, 2019
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
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