Today's networks consist of many autonomous entities that follow their own objectives, i.e., smart devices or parts of large AI systems, that are interconnected. Given the size and complexity of most communication networks, each entity typically only has a local view and thus must rely on a local routing protocol for sending and forwarding packets. A common solution for this is greedy routing, where packets are locally forwarded to a neighbor in the network that is closer to the packet's destination. In this paper we investigate a game-theoretic model with autonomous agents that aim at forming a network where greedy routing is enabled. The agents are positioned in a metric space and each agent tries to establish as few links as possible, while maintaining that it can reach every other agent via greedy routing. Thus, this model captures how greedy routing networks are formed without any assumption on the distribution of the agents or the specific employed greedy routing protocol. Hence, it distills the essence that makes greedy routing work. We study two variants of the model: with directed edges or with undirected edges. For the former, we show that equilibria exist, have optimal total cost, and that in Euclidean metrics they can be found efficiently. However, even for this simple setting computing optimal strategies is NP-hard. For the much more challenging setting with undirected edges, we show for the realistic setting with agents in 2D Euclidean space that the price of anarchy is between 1.75 and 1.8 and for higher dimensions it is less than 2. Also, we show that best response dynamics may cycle, but that in Euclidean space almost optimal approximate equilibria can be computed in polynomial time. Moreover, for 2D Euclidean space, these approximate equilibria outperform the well-known Delaunay triangulation.

翻译：当今网络由众多遵循自身目标的自主实体（如智能设备或大型人工智能系统的组成部分）互联而成。鉴于大多数通信网络的规模与复杂性，每个实体通常仅具备局部视图，因此必须依赖本地路由协议进行数据包的发送与转发。贪婪路由是解决该问题的常见方案，即数据包在本地被转发至网络中距离其目的地更近的邻居节点。本文研究一种博弈论模型，其中自主智能体旨在构建支持贪婪路由的网络。智能体分布于度量空间中，每个智能体在维持可通过贪婪路由抵达其他所有智能体的前提下，试图建立尽可能少的连接。该模型揭示了贪婪路由网络的形成机制，且无需对智能体分布或具体采用的贪婪路由协议作任何假设，从而提炼出贪婪路由运作的本质原理。我们研究该模型的两种变体：有向边模型与无向边模型。针对前者，我们证明均衡状态存在且具有最优总成本，在欧氏度量空间中可高效求解；但即使在此简单设定下，计算最优策略仍是NP难问题。针对更具挑战性的无向边模型，我们在智能体分布于二维欧氏空间的实际场景中证明无政府代价介于1.75至1.8之间，更高维度下则小于2。同时，我们证明最优响应动态可能产生循环，但在欧氏空间中可在多项式时间内计算出近似最优的近似均衡解。此外在二维欧氏空间中，这些近似均衡解的性能优于著名的Delaunay三角剖分。