  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.
