Aspects of Wardrop equilibria

Global communication networks like the Internet often lack a central authority that monitors and regulates network traffic. Mostly even cooperation among network users is not possible. Network users may behave selfishly according to their private interest without regard to the overall system performance. Such highly complex environments prompted a paradigm shift in computer science. Whereas traditional concepts are designed for stand-alone machines and manageable networks, a profound understanding of large-scale communication systems with strategic users requires to combine methods from theoretical computer science with game-theoretic techniques. This motivates the analysis of network traffic in the framework of non-cooperative game theory. The principal aspect of this theory is the notion of equilibrium that describes stable outcomes of a non-cooperative game. In his seminal paper, Wardrop introduced a game-theoretic model in the 1950s for describing resource sharing problems in the context of road traffic systems. Wardrop’s traffic model has attracted a lot of interest and inspired a great deal of research, especially after the emergence of huge non-cooperative systems like the Internet. In this thesis, we follow this line of research and study equilibrium situations in Wardrop’s traffic model. In Wardrop’s model a rate of traffic between each pair of vertices of a network is modeled as network flow, i. e., traffic is allowed to split into arbitrary pieces. The resources are the network edges with latency functions quantifying the time needed to traverse an edge. The latency of an edge depends on the congestion. It increases the more flow traverses that edge. A common interpretation of the Wardrop model is that flow is controlled by an infinite number of agents each of which is responsible to route an infinitesimal amount of traffic between its origin and destination vertex. Each agent plays a pure strategy in choosing one path from its origin to its destination, where the agent’s disutility is the sum of edge latencies on this path. Note that this game-theoretic model permits extremely complex mutual dependencies among the agents’ disutilities precluding application of standard optimization methods. A solution concept for this network game is provided by the theory of Wardrop equilibria. A Wardrop equilibrium denotes a strategy profile in which all used paths between a given