Geometric Selfish Network Creation (GEONET)

许多重要的网络，最突出的是互联网或(在线)社交网络，都不是由中央设计创建的，也没有管理它们的中央权威机构。相反，这样的网络是由许多自私的代理人不协调的相互作用产生的，这些代理人可能会修改网络的一部分，以适应他们的个人需求。在理论计算机科学、数学和经济学的交叉中，最近的一个研究趋势是从博弈论的角度对这种网络的创建进行建模和分析。网络的创建过程被认为是一个非合作的战略博弈，新兴网络是从博弈的均衡状态衍生出来的。在过去的二十年里，许多这样的模型被提出和分析，但它们都包含了强有力的简化假设，并且它们的一些预测与来自真实世界网络的经验观察不一致。其中一个主要原因是以前的工作忽略了现实世界网络中的节点位于某个潜在的(通常是度量的)空间中，并且这种几何设置对所创建的网络具有很强的影响。在此提出的项目旨在通过调查底层几何图形作为新特征的影响，向更现实的自私网络创建模型迈出下一步。这使得可以对从光纤通信网络到(在线)社交网络的各种网络的创建进行建模和分析。在该研究项目中获得的见解将导致对各种类型的真实世界网络的更好的理解，并且它们对于设计新的(分布式)算法来分散地创建高效和健壮的通信网络将是有价值的。

Many important networks, most prominently the Internet or (online) social networks, have not been created by central design and there is no central authority governing them. Instead, such networks emerged from the uncoordinated interaction of many selfish agents which may modify parts of the networks to suit their individual needs. A recent research trend in the intersection of Theoretical Computer Science, Mathematics and Economics is to model and analyze the creation of such networks from a game-theoretic point of view. The network creation process is considered as a non-cooperative strategic game and the emerging networks are derived from the game's equilibrium states. In the last two decades many such models have been proposed and analyzed but all of them incorporate strong simplifying assumptions and some of their predictions are not in line with empirical observations from real-world networks. One of the main reasons for this is that previous work neglected that nodes in real-world networks are located in some underlying (usually metric) space and that this geometric setting has a strong influence on the created networks. The hereby proposed project aims at taking the next step towards more realistic models for selfish network creation by investigating the impact of an underlying geometry as novel feature. This allows to model and to analyze the creation of diverse networks ranging from fiber-optic communication networks to (online) social networks.The insights gained in this research project shall lead to an improved understanding of various types of real-world networks and they shall be valuable for designing new (distributed) algorithms for the decentralized creation of efficient and robust communication networks.