Overview
Part of the book series: Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics (MOW)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Anja Schedel analyzes two models in the field of algorithmic game theory which both constitute bilevel problems in networks. The first model is a game-theoretic variant of the well-known Steiner forest problem, and one is interested in an optimal sharing of the cost of the Steiner forest. The author provides (and partially exactly characterizes) network structures which allow for cost-minimal pure Nash equilibria. The second model is motivated from privatized public roads, in which private, selfishly acting firms build roads, and as compensation for their investment, are allowed to set prices for using the roads. For a basic model of this situation, the author shows existence and uniqueness of pure Nash equilibria. The existence result requires a non-standard proof approach since techniques like Kakutani’s fixed point theorem cannot be applied directly.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Cost Sharing, Capacity Investment and Pricing in Networks
Authors: Anja Schedel
Series Title: Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics
DOI: https://doi.org/10.1007/978-3-658-33170-2
Publisher: Springer Spektrum Wiesbaden
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021
Softcover ISBN: 978-3-658-33169-6Published: 29 June 2021
eBook ISBN: 978-3-658-33170-2Published: 28 June 2021
Series ISSN: 2523-7926
Series E-ISSN: 2523-7934
Edition Number: 1
Number of Pages: VIII, 236
Number of Illustrations: 94 b/w illustrations
Topics: Continuous Optimization, Algorithms, Applications of Mathematics