Strategic Network Creation for Enabling Greedy Routing

In this paper, we present the first game-theoretic network creation model that incorporates greedy routing, i.e., the agents in our model are embedded in some metric space and strive for creating a network where all-pairs greedy routing is enabled. In contrast to graph-theoretic shortest paths, our agents route their traffic along greedy paths, which are sequences of nodes where the distance in the metric space to the respective target node gets strictly smaller by each hop. Besides enabling greedy routing, the agents also optimize their connection quality within the created network by constructing greedy paths with low stretch. This ensures that greedy routing is always possible in equilibrium networks, while realistically modeling the agents' incentives for local structural changes to the network. With this we augment the elegant network creation model by Moscibroda, Schmidt, and Wattenhofer (PODC'06) with the feature of greedy routing. For our model, we analyze the existence of (approximate)-equilibria and the computational hardness in different underlying metric spaces. E.g., we characterize the set of equilibria in 1-2-metrics and tree metrics, we show that in both metrics Nash equilibria always exist, and we prove that the well-known $\Theta$-graph construction yields constant-approximate Nash equilibria in Euclidean space. The latter justifies distributed network construction via $\Theta$-graphs from a new point-of-view, since it shows that this powerful technique not only guarantees networks having a low stretch but also networks that are almost stable.