AI 中文总结
研究存在预先对齐代理组的合作博弈，通过连通性增强局部值的沙普利值建模局部连接对网络连通性的贡献，并将其与色多项式、图特多项式及Potts模型配分函数相联系，以解决相关网络问题。
AI 中文摘要
我们开启了对存在预先对齐代理组的合作博弈的研究。例如，在道路网络中，代理是十字路口，预先对齐的组是路段；对于数据集，代理是属性，连接两个（或更多）属性的每个数据库是预先对齐的。本文中每个预先对齐的组大小为二。我们的目标是找到一种方法来确定每个单独的局部连接（预先对齐的对）对网络连通性的贡献，可用于考虑对抗攻击、规划网络防御或在网络的各个局部连接所有者之间分配利润。我们通过连通性增强的“局部值”的沙普利值来建模这些贡献，这些局部值是由例如局部连接的失败概率确定的特征函数。我们将这些连通性增强局部值的势和沙普利值的概念与色多项式、图特多项式以及统计物理学中Potts模型的配分函数联系起来。
英文摘要
We initiate the study of cooperative games where there exist groups of pre-aligned agent. For example, in a road network, the agents are cross-roads and pre-aligned groups are road-segments. For a set of datasets, the agents are attributes and each database which connects two (or more) attributes is pre-aligned. In this paper, each pre-aligned group has size two. Our goal is to find a way to determine the contribution of each individual local connection (pre-aligned couple) to the connectivity of the network, having an adversarial attack in mind or planning a defense of the network, or wanting to split the profits of the network between various owners of the individual local connections of the network. We model these contributions by Shapley values of the connectivity augmented 'local values' which are characteristic functions determined, e.g., by failure probabilities of local connections. We link the concepts of potential and Shapley values of these connectivity augmented local values to the world of chromatic and Tutte polynomials and the partition function of the Potts model from statistical physics.
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