[论文解读] Optimal mechanisms for distributed resource-allocation.

Rahul Chandan, Dario Paccagnan+1 more|arXiv (Cornell University)|Nov 18, 2019

Auction Theory and Applications被引用 4

一句话总结

本文引入广义光滑性（generalized smoothness），这是一种新颖的框架，通过实现更紧密且更广泛适用的效率保证，改进了分布式资源分配博弈中的价之失（price-of-anarchy）界。它证明了在局部成本分摊博弈中，价之失可通过可处理的线性规划被精确表征和优化，从而涵盖并推广了先前的结果。

ABSTRACT

As the complexity of real-world systems continues to increase, so does the need for distributed protocols that are capable of guaranteeing a satisfactory system performance, without the reliance on centralized decision making. In this respect, game theory provides a valuable framework for the design of distributed algorithms in the form of equilibrium efficiency bounds. Arguably one of the most widespread performance metrics, the price-of-anarchy measures how the efficiency of a system degrades when moving from centralized to distributed decision making. While the smoothness framework -- introduced in Roughgarden 2009 -- has emerged as a powerful methodology for bounding the price-of-anarchy, the resulting bounds are often conservative, bringing into question the suitability of the smoothness approach for the design of distributed protocols. In this paper, we introduce the notion of generalized smoothness in order to overcome these difficulties. First, we show that generalized smoothness arguments are more widely applicable, and provide tighter price-of-anarchy bounds compared to those obtained using the existing smoothness framework. Second, we show how to leverage the notion of generalized smoothness to obtain a tight characterization of the price-of-anarchy, relative to the class of local cost-sharing games. Within this same class of games we show that the price-of-anarchy can be computed and optimized through the solution of a tractable linear program. Finally, we demonstrate that our approach subsumes and generalizes existing results for three well-studied classes of games.

研究动机与目标

• 解决经典光滑性框架在界定分布式系统中价之失时的局限性。
• 开发一种更广泛适用且更紧密的方法，以分析去中心化决策中的效率损失。
• 通过可处理的优化方法，表征并优化局部成本分摊博弈中的价之失。
• 统一并推广在三个经典博弈类中已有的研究成果。

提出的方法

• 将广义光滑性概念作为博弈论中经典光滑性框架的扩展提出。
• 构建一个线性规划模型，以计算并优化局部成本分摊博弈中的价之失。
• 证明广义光滑性论证可产生比经典光滑性更紧的价之失界。
• 证明在指定博弈类中，价之失可通过线性规划被精确计算和优化。
• 证明广义光滑性框架涵盖并推广了在三个典型博弈类中的先前结果。

实验结果

研究问题

• RQ1 广义光滑性是否能提供比经典光滑性框架更紧且更广泛适用的价之失界？
• RQ2 在局部成本分摊博弈类中，价之失是否可被精确计算和优化？
• RQ3 广义光滑性方法是否能统一并推广多个经典博弈类中的现有研究成果？
• RQ4 广义光滑性与分布式资源分配中最优机制设计之间存在何种关系？

主要发现

• 广义光滑性相较于经典光滑性框架，可显著收紧价之失界。
• 在局部成本分摊博弈中，价之失可通过一个可处理的线性规划被精确计算和优化。
• 所提出的框架涵盖并推广了在三个经典博弈类中的现有研究成果。
• 该方法可对去中心化资源分配中的系统效率损失实现紧密表征。