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 (CULO), 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 CULO 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 that the CULO model 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，Wardrop均衡（WE）始终缺乏坚实的行为基础。为强化这一基础，必须正视人类决策过程中的有界理性，例如缺乏准确信息、有限计算能力及次优选择。然而，文献中这种对行为完美主义的退让通常伴随着对WE概念的修正。本文证明，放弃完全理性未必需要背离WE。相反，在有界理性出行者参与的路径博弈中，WE能够以全局稳定性方式达到。我们通过构建一种逐日（DTD）动态模型实现这一结果，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及选择概率。我们提出的累积Logit（CULO）模型虽与经典DTD模型类似，但做出了关键变革：经典模型假设路径估值基于历史数据的平均成本，而我们的模型则基于累积成本进行估值。为描述路径选择行为，CULO模型仅使用两个参数——一个表征未来路径成本相对于历史成本的折现率，另一个表征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，CULO模型均能收敛至WE。因此，本理论既维护了WE作为交通系统分析基准的地位，又通过解释为何WE状态下同等优质的路径会被以不同概率选择，解决了Harsanyi不稳定性问题带来的理论挑战。