Approximate pure nash equilibria in congestion, opinion formation and facility location games / submitted by Matthias Feldotto ; [Advisor: Assistant Professor Dr. Alexander Skopalik, Reviewers: Assistant Professor Dr. Alexander Skopalik, Senior Lecturer Dr. Martin Gairing, Members of the Doctoral Panel: Prof. Dr. Friedhelm Meyer auf der Heide, Assistant Professor Dr. Alexander Skopalik, Senior Lecturer Dr. Martin Gairing, Prof. Dr. Claus-Jochen Haake, Dr. Rainer Feldmann]. Paderborn, 2019
Content
- Abstract
- Zusammenfassung
- Contents
- Preface
- Introduction
- Preliminaries
- Computation of Approximate Pure Nash Equilibria
- Congestion Games
- Unweighted Congestion Games
- Model and Further Notations
- Approximating the Potential
- Computation of Approximate Pure Nash Equilibria
- Shapley Value Weighted Congestion Games
- Model and Further Notations
- Shapley and Potential Properties
- Approximating Shapley with Proportional Cost-Shares
- Approximate Price of Anarchy and Stretch
- Computation of Approximate Pure Nash Equilibria
- Sampling the Shapley Value
- Existence of Approximate Pure Nash Equilibria
- Further Applications and Discussion
- Bibliography
- Nomenclature