Wardrop均衡可以是有界理性的：一种新的路径选择行为理论
Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice
AI总结：
本研究提出累积Logit（CumLog）逐日动态模型，证明有界理性出行者可通过该模型在全局稳定性下达到Wardrop均衡，无需修改均衡概念，并解决了Harsanyi不稳定问题。
摘要：
作为交通科学中最基本的概念之一，Wardrop均衡（WE）一直缺乏较强的行为基础。为了加强这一基础，必须考虑人类决策过程中的有界理性，例如缺乏准确信息、有限的计算能力以及次优选择。然而，文献中这种从行为完美主义的退却，通常伴随着对WE的概念性修改。在此，我们表明放弃完全理性并不必然导致偏离WE。相反，在有界理性出行者参与的路径选择博弈中，WE可以以全局稳定性达到。我们通过开发一种逐日（DTD）动态模型来实现这一结果，该模型模拟了出行者如何根据过去的经验逐渐调整其路径估值，进而调整选择概率。我们的模型称为累积Logit（CumLog），类似于经典的DTD模型，但做出了一个关键改变：经典模型假设路径基于历史数据的平均成本来估值，而我们的模型则基于累积成本来估值路径。为了描述路径选择行为，CumLog模型仅使用两个参数，一个参数用于解释未来路径成本相对于过去成本在估值中的折扣率，另一个参数描述路径选择概率对估值差异的敏感性。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总是收敛到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。它还通过解释为什么在WE处同样好的路径以不同概率被选择，解决了Harsanyi不稳定问题所带来的理论挑战。
英文摘要：
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.
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