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 with 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 attention on multi-commodity 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 product-union 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载荷随需求变化时的单调性。主要目标是识别能够排除悖论性非单调行为存在的条件。对于单商品路由博弈而言，网络拓扑是决定单调性的唯一因素；与此不同，在具有多商品的一般拥塞博弈中，策略集的结构起着关键作用。我们在拥塞博弈的通用框架下展开研究，特别关注多商品单元素拥塞博弈，并证明在此类博弈中均衡载荷关于每一需求均具有单调性。进一步地，我们给出了均衡载荷共单调性的条件，即研究需求变化后所有均衡载荷是否同时增加或减少。最后，我们将研究从单元素拥塞博弈推广至更大类的乘积-并集拥塞博弈，其结构类似于串并联网络的概念。