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.

翻译：在本文中，我们提出了首个融合贪婪路由的博弈论网络构建模型。该模型中，智能体嵌入于某个度量空间中，致力于创建所有节点对间贪婪路由可行的网络。与基于图论的最短路径不同，智能体沿贪婪路径传输流量——此类路径由节点序列构成，其中每个跳步在度量空间内到目标节点的距离严格递减。除实现贪婪路由外，智能体还通过构建低拉伸度的贪婪路径优化其连接质量，这既确保均衡网络中贪婪路由始终可行，又真实刻画了智能体进行局部网络结构变化的激励。据此，我们在Moscibroda、Schmidt与Wattenhofer（PODC'06）提出的优雅网络构建模型中增加了贪婪路由特性。针对该模型，我们分析了不同底层度量空间下（近似）均衡的存在性及计算复杂度。例如，我们刻画了1-2度量与树度量中的均衡集合，证明在这两种度量中纳什均衡始终存在，并证明著名的$\Theta$-图构造在欧氏空间中能产生常数近似纳什均衡。后者从一个全新视角验证了基于$\Theta$-图的分布式网络构建的合理性，表明这一强大技术不仅能保证网络具有低拉伸度，还能确保网络接近稳定状态。