This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior can be excluded. In contrast to routing games with a single commodity, where the network topology is the sole determinant factor for monotonicity, for general congestion games with multiple commodities the structure of the strategy sets plays a crucial role. We frame our study in the general setting of congestion games, with a special focus on singleton congestion games, for which we establish the monotonicity of equilibrium loads with respect to every demand. We then provide conditions for comonotonicity of the equilibrium loads, i.e., we investigate when they jointly increase or decrease after variations of the demands. We finally extend our study from singleton congestion games to the larger class of constrained series-parallel congestion games, whose structure is reminiscent of the concept of a series-parallel network.

翻译：本文研究非原子拥塞博弈中均衡成本与均衡负载随需求变化的单调性，主要目标是识别可排除悖论性非单调行为成立的条件。与单一商品路由博弈（其单调性仅由网络拓扑结构决定）不同，多商品一般拥塞博弈中策略集的结构对单调性起关键作用。本文在拥塞博弈的通用框架下展开研究，重点聚焦于单点拥塞博弈，并针对此类博弈建立了均衡负载关于任意需求的单调性。随后给出均衡负载共单调性的充分条件，即探究需求变化时均衡负载何时会同步增减。最后将研究从单点拥塞博弈拓展至受约束的串并联拥塞博弈这一更广泛的类别，此类博弈的结构与串并联网络概念相呼应。