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Braess' paradox: A cooperative game-theoretic point of view
Networks ( IF 2.1 ) Pub Date : 2021-01-25 , DOI: 10.1002/net.22018
Mauro Passacantando 1 , Giorgio Gnecco 2 , Yuval Hadas 3 , Marcello Sanguineti 4
Affiliation  

Braess' paradox is a classical result in the theory of congestion games. It motivates theoretically why adding a resource (e.g., an arc) to a network may sometimes worsen, rather than improve, the overall network performance. Differently from previous literature, which studies Braess' paradox in a non-cooperative game-theoretic setting, in this work, a framework is proposed to investigate its occurrence by exploiting cooperative games with transferable utility (TU games) on networks. In this way, instead of focusing on the marginal contribution to the network utility provided by the insertion of an arc when a single initial scenario is considered, the arc average marginal utility with respect to various initial scenarios, that is, its Shapley value in a suitably-defined TU game, is evaluated. It is shown that, for choices of the utility function of the TU game modeling congestion, there are cases for which the Shapley value associated with an arc is negative, meaning that its average marginal contribution to the network utility is negative.

中文翻译:

布雷斯悖论:合作博弈论的观点

Braess 悖论是拥塞博弈理论中的经典结果。它在理论上激发了为什么向网络添加资源(例如,弧)有时会恶化而不是改善整体网络性能。与之前在非合作博弈论环境中研究布雷斯悖论的文献不同,在这项工作中,提出了一个框架,通过利用网络上具有可转移效用的合作博弈(TU 博弈)来研究其发生。这样,在考虑单个初始场景时,不是关注通过插入弧对网络效用的边际贡献,而是弧相对于各种初始场景的平均边际效用,即它在 a 中的 Shapley 值适当定义的 TU 游戏,进行评估。结果表明,
更新日期:2021-01-25
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