📝 SummarXiv

Abstract

Studying the impact of cooperation in strategic settings is one of the cornerstones of algorithmic game theory. Intuitively, allowing more cooperation yields equilibria that are more beneficial for the society of agents. However, for many games it is still an open question how much cooperation is actually needed to ensure socially good equilibria. We contribute to this research endeavor by analyzing the benefits of cooperation in a network formation game that models the creation of communication networks via the interaction of selfish agents. In our game, agents that correspond to nodes of a network can buy incident edges of a given weighted host graph to increase their centrality in the formed network. The cost of an edge is proportional to its length, and both endpoints must agree and pay for an edge to be created. This setting is known for having a high price of anarchy. To uncover the impact of cooperation, we investigate the price of anarchy of our network formation game with respect to multiple solution concepts that allow for varying amounts of cooperation. On the negative side, we show that on host graphs with arbitrary edge weights even the strongest form of cooperation cannot improve the price of anarchy. In contrast to this, as our main result, we show that cooperation has a significant positive impact if the given host graph has metric edge weights. For this, we prove asymptotically tight bounds on the price of anarchy via a novel proof technique that might be of independent interest and can be applied in other models with metric weights.