<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 Public License.

{"article-title":"Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions"}

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow...

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Published Online: Aug 23, 2019

Page range: 331 - 350

Received: Mar 05, 2019

Accepted: Apr 25, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00029

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

© 2019 F. B. Benli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Published Online: Aug 23, 2019

Page range: 331 - 350

Received: Mar 05, 2019

Accepted: Apr 25, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00029

KeywordsShapley-Folkman theorem, asymmetric auctions, Backward shooting method, auction solving, fixed point iterations

© 2019 F. B. Benli et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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