In this paper, we present a new model of congestion games with finite and random number of players, and an analytical method to compute the random path and link flows. We study the equilibrium condition, reformulate it as an equivalent variational inequality problem, and establish the existence and non-uniqueness of the equilibria. We also upper bound the price of anarchy with affine cost functions to characterize the quality of the equilibria. The upper bound is tight in some special cases, including the case of deterministic players. Finally a general lower bound is also provided.

中文翻译：

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具有随机参与者的原子拥塞游戏：网络平衡和无政府状态的价格

在本文中，我们提出了一种具有有限和随机数量玩家的拥塞游戏模型，以及一种计算随机路径和链接流的分析方法。我们研究平衡条件，将其重新表述为等效的变分不等式问题，并建立平衡的存在性和非唯一性。我们还用仿射成本函数将无政府状态的价格上限确定了均衡质量的特征。在某些特殊情况下（包括确定性参与者），上限很紧。最后，还提供了一般的下限。