Deriving the Pure Price of Anarchy for Networked Resource Allocation Games

2026-09-10

AI Summary

本文通过线性规划方法，为任意信息网络和系统目标设计最优局部效用函数，以优化纯价格无政府状态（pPoA）性能保证。

Abstract

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.

Problem

• multi-agent coordination
• pure price of anarchy
• utility functions
• information networks
• system objective

Innovation

• pure price of anarchy
• utility design
• information network
• supermodular objective functions
• submodular system objectives