As one of the most fundamental concepts in transportation science, Wardrop equilibrium (WE) has always had a relatively weak behavioral underpinning. To strengthen this foundation, one must reckon with bounded rationality in human decision-making processes, such as the lack of accurate information, limited computing power, and sub-optimal choices. This retreat from behavioral perfectionism in the literature, however, was typically accompanied by a conceptual modification of WE. Here, we show that giving up perfect rationality need not force a departure from WE. On the contrary, WE can be reached with global stability in a routing game played by boundedly rational travelers. We achieve this result by developing a day-to-day (DTD) dynamical model that mimics how travelers gradually adjust their route valuations, hence choice probabilities, based on past experiences. Our model, called cumulative logit (CumLog), resembles the classical DTD models but makes a crucial change: whereas the classical models assume routes are valued based on the cost averaged over historical data, ours values the routes based on the cost accumulated. To describe route choice behaviors, the CumLog model only uses two parameters, one accounting for the rate at which the future route cost is discounted in the valuation relative to the past ones and the other describing the sensitivity of route choice probabilities to valuation differences. We prove tha CumLog always converges to WE, regardless of the initial point, as long as the behavioral parameters satisfy certain mild conditions. Our theory thus upholds WE's role as a benchmark in transportation systems analysis. It also resolves the theoretical challenge posed by Harsanyi's instability problem by explaining why equally good routes at WE are selected with different probabilities.

翻译：作为交通科学中最基本的概念之一，瓦德罗普均衡（WE）一直缺乏坚实的行为基础。为加强这一基础，必须考虑人类决策过程中的有限理性，例如缺乏准确信息、计算能力有限以及非最优选择。然而，文献中这种对行为完美主义的退让通常伴随着对WE的概念修改。本文表明，放弃完全理性并不必然要求偏离WE。相反，在有限理性出行者参与的路径博弈中，WE能够全局稳定地达到。我们通过建立一种逐日（DTD）动力学模型实现了这一结果，该模型模拟出行者如何基于过往经验逐步调整其路径估值，进而调整选择概率。我们的模型称为累积逻辑模型（CumLog），与经典DTD模型相似，但做出了关键改变：经典模型假设路径基于历史数据的平均成本进行估值，而我们的模型基于累积成本进行估值。为描述路径选择行为，CumLog模型仅使用两个参数：一个参数刻画路径估值中未来成本相对于过去成本的折扣率，另一个参数描述路径选择概率对估值差异的敏感度。我们证明，只要行为参数满足某些温和条件，无论初始点如何，CumLog始终收敛于WE。因此，我们的理论维护了WE作为交通系统分析基准的作用。同时，通过解释为什么WE中同等优质的路径会以不同概率被选择，该理论解决了Harsanyi稳定性问题带来的理论挑战。