{"title":"Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice","authors":"Jiayang Li, Zhaoran Wang, Yu (Marco) Nie","doi":"10.1287/trsc.2023.0132","DOIUrl":null,"url":null,"abstract":"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 suboptimal 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 that routes are valued based on the cost averaged over historical data, our model 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 that the CumLog 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 explains why equally good routes at equilibrium may be selected with different probabilities, which solves the instability problem posed by Harsanyi.Funding: This research is funded by the National Science Foundation [Grants CMMI #2225087 and ECCS #2048075].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0132 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transportation Science","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1287/trsc.2023.0132","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
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 suboptimal 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 that routes are valued based on the cost averaged over historical data, our model 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 that the CumLog 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 explains why equally good routes at equilibrium may be selected with different probabilities, which solves the instability problem posed by Harsanyi.Funding: This research is funded by the National Science Foundation [Grants CMMI #2225087 and ECCS #2048075].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0132 .
期刊介绍:
Transportation Science, published quarterly by INFORMS, is the flagship journal of the Transportation Science and Logistics Society of INFORMS. As the foremost scientific journal in the cross-disciplinary operational research field of transportation analysis, Transportation Science publishes high-quality original contributions and surveys on phenomena associated with all modes of transportation, present and prospective, including mainly all levels of planning, design, economic, operational, and social aspects. Transportation Science focuses primarily on fundamental theories, coupled with observational and experimental studies of transportation and logistics phenomena and processes, mathematical models, advanced methodologies and novel applications in transportation and logistics systems analysis, planning and design. The journal covers a broad range of topics that include vehicular and human traffic flow theories, models and their application to traffic operations and management, strategic, tactical, and operational planning of transportation and logistics systems; performance analysis methods and system design and optimization; theories and analysis methods for network and spatial activity interaction, equilibrium and dynamics; economics of transportation system supply and evaluation; methodologies for analysis of transportation user behavior and the demand for transportation and logistics services.
Transportation Science is international in scope, with editors from nations around the globe. The editorial board reflects the diverse interdisciplinary interests of the transportation science and logistics community, with members that hold primary affiliations in engineering (civil, industrial, and aeronautical), physics, economics, applied mathematics, and business.