Theoretical and Computational Aspects of Resource Allocation Games

We investigate the impact of Stackelberg routing to reduce the price of anarchy innetwork routing games. In this setting, an α fraction of the entire demand is first routed centrallyaccording to a predefined Stackelberg strategy and the remaining demand is then routed selfishlyby (nonatomic) players. Although several advances have been made recently in proving thatStackelberg routing can in fact significantly reduce the price of anarchy for certain networktopologies, the central question of whether this holds true in general is still open. We answerthis question negatively by constructing a family of single-commodity instances such that everyStackelberg strategy induces a price of anarchy that grows linearly with the size of the network.Moreover, we prove upper bounds on the price of anarchy of the Largest-Latency-First (LLF)strategy that only depend on the size of the network. Besides other implications, this rules outthe possibility to construct constant-size networks to prove an unbounded price of anarchy. Inlight of this negative result, we consider bicriteria bounds. We develop an efficiently computableStackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow withrespect to demands scaled by a factor of 1 +√1− α. Finally, we analyze the effectiveness of aneasy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class oflatency functions that includes polynomial latency functions as a special case. Our analysis isbased on an approach which is simple, yet powerful enough to obtain (almost) tight bounds forSCALE in general networks.