推导网络化资源分配博弈的纯无政府状态价格

中文摘要 AI 辅助

本研究采用博弈论方法，考虑了代理之间具有任意信息网络的多代理协调问题。系统设计者旨在为代理分配局部效用函数，以引导其行动朝向期望的系统目标。所分配局部效用的性能通过众所周知的纯无政府状态价格（pPoA）指标来衡量，该指标等于相应博弈的最差纯纳什均衡下的系统目标与最优系统目标之比。我们的目标是推导出对于任何给定信息网络和系统目标，优化基于pPoA的性能保证的效用函数。我们开发了一个线性规划，用于推导任意信息网络和任意系统目标的最优pPoA。我们的工作是首个解决任意网络的最优效用设计问题；我们的技术推广了先前仅考虑完全信息设置的方法。对于超模目标函数，我们证明了一个反直觉的结果：无论原始信息网络如何，完全禁止通信的效用设计是最优的。对于子模系统目标，详尽的数值分析表明，即使在这种情况下，最优效用设计对通信故障也具有鲁棒性。当系统目标是加权最大覆盖时，边际贡献效用设计被证明能在多种感兴趣的信息网络上优化pPoA。

英文摘要

This work considers multi-agent coordination with arbitrary information networks among the agents using a game-theoretic approach. A system designer aims to assign local utility functions to the agents to guide their actions toward a desired system objective. The performance of the assigned local utilities is measured by the well known pure price of anarchy (pPoA) metric that equals the ratio of the system objective at the worst pure Nash equilibrium of the corresponding game to the optimal system objective. Our aim is to derive the utility functions which optimize the pPoA-based performance guarantees for any given information network and system objective. We develop a linear program that derives the optimal pPoA for any arbitrary information network and arbitrary system objective. Our work is the first to solve optimal utility design for arbitrary networks; our techniques generalize previous approaches which considered only the full-information setting. For supermodular objective functions, we prove that counterintuitively, a fully communication-denied utility design is optimal irrespective of the original information network. For submodular system objectives, an exhaustive numerical analysis suggests that the optimal utility design is robust to communication failures even for this case. When the system objective is weighted maximum coverage, the marginal contribution utility design provably optimizes the pPoA for a wide variety of information networks of interest.

发表机构

• University of Colorado Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校）
• Politecnico di Torino（都灵理工大学）

机构由 AI 辅助整理，请以论文原文为准。