论文标题
合作网络和Hodge-Shapley价值
Cooperative networks and Hodge-Shapley value
论文作者
论文摘要
劳埃德·沙普利（Lloyd Shapley）的合作价值分配理论是游戏理论中的一个核心概念，在各个领域广泛使用，以分发资源，评估个人贡献并确保公平。莎普利的价值公式和他的四个公理构成了理论的基础。 传统上，莎普利价值是根据合作游戏中所有玩家最终组成大联盟的假设。在本文中，我们将Shapley值重新解释为对某个随机路径积分的期望，每个路径代表一般的联盟形成过程。结果，价值分配自然扩展到所有部分联盟国家。另外，我们提供了一组五个属性，这些属性扩展了沙普利公理并表征了随机路径积分。最后，通过将霍奇演算，随机过程和边缘流的路径集成在图上，我们将合作价值分配理论扩展到标准联盟游戏结构之外，以涵盖更广泛的合作网络配置。
Lloyd Shapley's cooperative value allocation theory stands as a central concept in game theory, extensively utilized across various domains to distribute resources, evaluate individual contributions, and ensure fairness. The Shapley value formula and his four axioms that characterize it form the foundation of the theory. Traditionally, the Shapley value is assigned under the assumption that all players in a cooperative game will ultimately form the grand coalition. In this paper, we reinterpret the Shapley value as an expectation of a certain stochastic path integral, with each path representing a general coalition formation process. As a result, the value allocation is naturally extended to all partial coalition states. In addition, we provide a set of five properties that extend the Shapley axioms and characterize the stochastic path integral. Finally, by integrating Hodge calculus, stochastic processes, and path integration of edge flows on graphs, we expand the cooperative value allocation theory beyond the standard coalition game structure to encompass a broader range of cooperative network configurations.
