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.

Autorentext

Anja Schedel received her PhD from the University of Augsburg in Germany. She is currently working as a postdoctoral researcher at the University of Augsburg. Her main research interests lie within the field of algorithmic game theory and include, in particular, cost sharing, bilevel optimization, and flows over time.

Inhalt
Introduction.- Preliminaries.- Cost Sharing in Networks.- Capacity and Price Competition in Networks.- Conclusion.