Martin Hoefer

Distributed Competition in Networks: Cost Sharing and Graph Clustering with Selfish Agents Martin Hoefer

This book treats two broad classes of non-cooperative games. They serve to analyze networks created and operated by distributed selfish agents. The goal is to advance the understanding of dynamics and trade-offs created by selfish incentives and influences of social networks on decision making. The analysis concentrates on existence, complexity, and social value of stable states like exact and approximate Nash equilibria. The first part of the book presents a class of games for cost sharing of a set of resources. Every player strives to satisfy a constraint on the purchased units with smallest investment. This framework is used to address networking aspects like service installation, facility location, or network design. The second part of the book studies graph clustering games. Every player is a vertex in a graph and chooses one of several possible clusters. The value of this decision depends on the decisions of other players and the graph. As a byproduct of the analysis it is shown that optimizing the popular clustering index Modularity is NP-hard. This provides the first fundamental insights into modularity optimization.