IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v67y2014icp86-108.html
   My bibliography  Save this article

Braess paradox under the boundedly rational user equilibria

Author

Listed:
  • Di, Xuan
  • He, Xiaozheng
  • Guo, Xiaolei
  • Liu, Henry X.

Abstract

The Braess paradox and its variants have been studied under the perfectly rational behavior assumption. However, when the perfect rationality assumption is relaxed to bounded rationality, which assumes that travelers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost, it remains unclear under what conditions the Braess paradox occurs. This paper fills this gap by exploring relationships between the occurrence of the Braess paradox and the indifference band as well as the demand level in the setting of the boundedly rational user equilibrium (BRUE). The definition of the Braess paradox is extended based on planners’ risk-taking attitudes, i.e., risk-averse, risk-prone and risk-neutral, due to the non-uniqueness of BRUE. The paradox occurrence conditions under different risk-taking attitudes are investigated using the classical Braess network and compared with those under the user equilibrium. Then we generalize the paradox conditions to simple and ordinary grid networks with regular Bureau of Public Roads (BPR) link performance functions. The impact of the link cost congestion sensitivity along with the indfference band on the occurrence of the Braess paradox is also studied.

Suggested Citation

  • Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.
    • Handle: RePEc:eee:transb:v:67:y:2014:i:c:p:86-108
    DOI: 10.1016/j.trb.2014.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261514000617
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2014.04.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jou, Rong-Chang & Lam, Soi-Hoi & Liu, Yu-Hsin & Chen, Ke-Hong, 2005. "Route switching behavior on freeways with the provision of different types of real-time traffic information," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(5), pages 445-461, June.
    2. Dietrich Braess & Anna Nagurney & Tina Wakolbinger, 2005. "On a Paradox of Traffic Planning," Transportation Science, INFORMS, vol. 39(4), pages 446-450, November.
    3. Dafermos, Stella & Nagurney, Anna, 1984. "On some traffic equilibrium theory paradoxes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 101-110, April.
    4. Fisk, Caroline, 1979. "More paradoxes in the equilibrium assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 305-309, December.
    5. Prashker, Joseph N. & Bekhor, Shlomo, 2000. "Some observations on stochastic user equilibrium and system optimum of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 277-291, May.
    6. Gao, Song & Frejinger, Emma & Ben-Akiva, Moshe, 2011. "Cognitive cost in route choice with real-time information: An exploratory analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 916-926, November.
    7. Richard Steinberg & Richard E. Stone, 1988. "The Prevalence of Paradoxes in Transportation Equilibrium Problems," Transportation Science, INFORMS, vol. 22(4), pages 231-241, November.
    8. Rapoport, Amnon & Kugler, Tamar & Dugar, Subhasish & Gisches, Eyran J., 2009. "Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox," Games and Economic Behavior, Elsevier, vol. 65(2), pages 538-571, March.
    9. Akamatsu, Takashi, 2000. "A dynamic traffic equilibrium assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 515-531, August.
    10. Hani S. Mahmassani & Gang-Len Chang, 1987. "On Boundedly Rational User Equilibrium in Transportation Systems," Transportation Science, INFORMS, vol. 21(2), pages 89-99, May.
    11. Yang, Hai & Bell, Michael G. H., 1998. "A capacity paradox in network design and how to avoid it," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 539-545, September.
    12. Cantillo, Víctor & Heydecker, Benjamin & de Dios Ortúzar, Juan, 2006. "A discrete choice model incorporating thresholds for perception in attribute values," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 807-825, November.
    13. Pas, Eric I. & Principio, Shari L., 1997. "Braess' paradox: Some new insights," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 265-276, June.
    14. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    15. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    16. Di, Xuan & Liu, Henry X. & Pang, Jong-Shi & Ban, Xuegang (Jeff), 2013. "Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 300-313.
    17. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.
    18. Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. (Walker) Wang, Wei & Wang, David Z.W. & Sun, Huijun & Feng, Zengzhe & Wu, Jianjun, 2016. "Braess Paradox of traffic networks with mixed equilibrium behaviors," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 95-114.
    2. Wang, Wei (Walker) & Wang, David Z.W. & Zhang, Fangni & Sun, Huijun & Zhang, Wenyi & Wu, Jianjun, 2017. "Overcoming the Downs-Thomson Paradox by transit subsidy policies," Transportation Research Part A: Policy and Practice, Elsevier, vol. 95(C), pages 126-147.
    3. Zhaolin Cheng & Laijun Zhao & Huiyong Li, 2020. "A Transportation Network Paradox: Consideration of Travel Time and Health Damage due to Pollution," Sustainability, MDPI, vol. 12(19), pages 1-22, October.
    4. S. F. A. Batista & Ludovic Leclercq, 2019. "Regional Dynamic Traffic Assignment Framework for Macroscopic Fundamental Diagram Multi-regions Models," Transportation Science, INFORMS, vol. 53(6), pages 1563-1590, November.
    5. Danczyk, Adam & Di, Xuan & Liu, Henry X. & Levinson, David M., 2017. "Unexpected versus expected network disruption: Effects on travel behavior," Transport Policy, Elsevier, vol. 57(C), pages 68-78.
    6. Yao, Jia & Cheng, Ziyi & Chen, Anthony, 2023. "Bibliometric analysis and systematic literature review of the traffic paradoxes (1968–2022)," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    7. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    8. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    9. Mahdi Takalloo & Changhyun Kwon, 2019. "On the Price of Satisficing in Network User Equilibria," Papers 1911.07914, arXiv.org.
    10. Di, Xuan & Ma, Rui & Liu, Henry X. & Ban, Xuegang (Jeff), 2018. "A link-node reformulation of ridesharing user equilibrium with network design," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 230-255.
    11. Di, Xuan & Liu, Henry X. & Ban, Xuegang (Jeff), 2016. "Second best toll pricing within the framework of bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 74-90.
    12. Yao, Jia & Huang, Wenhua & Chen, Anthony & Cheng, Zhanhong & An, Shi & Xu, Guangming, 2019. "Paradox links can improve system efficiency: An illustration in traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 35-49.
    13. Eikenbroek, Oskar A.L. & Still, Georg J. & van Berkum, Eric C. & Kern, Walter, 2018. "The Boundedly Rational User Equilibrium: A parametric analysis with application to the Network Design Problem," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 1-17.
    14. Aalami, Soheila & Kattan, Lina, 2022. "Proportionally fair flow markets for transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 24-41.
    15. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    16. Di, Xuan & Ban, Xuegang Jeff, 2019. "A unified equilibrium framework of new shared mobility systems," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 50-78.
    17. Ashraf, Muhammad Hasan & Chen, Yuwen & Yalcin, Mehmet G., 2022. "Minding Braess Paradox amid third-party logistics hub capacity expansion triggered by demand surge," International Journal of Production Economics, Elsevier, vol. 248(C).
    18. Xuan Di & Henry X. Liu & Shanjiang Zhu & David M. Levinson, 2017. "Indifference bands for boundedly rational route switching," Transportation, Springer, vol. 44(5), pages 1169-1194, September.
    19. Yao, Jia & Chen, Anthony, 2014. "An analysis of logit and weibit route choices in stochastic assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 31-49.
    20. Senlai Zhu & Jie Ma & Tianpei Tang & Quan Shi, 2020. "A Combined Modal and Route Choice Behavioral Complementarity Equilibrium Model with Users of Vehicles and Electric Bicycles," IJERPH, MDPI, vol. 17(10), pages 1-18, May.
    21. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.
    22. Alessandro Vacca & Carlo Giacomo Prato & Italo Meloni, 2019. "Should I stay or should I go? Investigating route switching behavior from revealed preferences data," Transportation, Springer, vol. 46(1), pages 75-93, February.
    23. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yao, Jia & Cheng, Ziyi & Chen, Anthony, 2023. "Bibliometric analysis and systematic literature review of the traffic paradoxes (1968–2022)," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    2. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.
    3. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    4. Yao, Jia & Chen, Anthony, 2014. "An analysis of logit and weibit route choices in stochastic assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 31-49.
    5. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    6. Wei-Hua Lin & Hong K. Lo, 2009. "Investigating Braess' Paradox with Time-Dependent Queues," Transportation Science, INFORMS, vol. 43(1), pages 117-126, February.
    7. Bittihn, Stefan & Schadschneider, Andreas, 2021. "The effect of modern traffic information on Braess’ paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    8. Shanjiang Zhu & David Levinson & Henry Liu, 2017. "Measuring winners and losers from the new I-35W Mississippi River Bridge," Transportation, Springer, vol. 44(5), pages 905-918, September.
    9. Di, Xuan & Liu, Henry X. & Pang, Jong-Shi & Ban, Xuegang (Jeff), 2013. "Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 300-313.
    10. Liang Wang & Lei Zhao & Xiaojian Hu & Xinyong Zhao & Huan Wang, 2023. "A Reliability-Based Traffic Equilibrium Model with Boundedly Rational Travelers Considering Acceptable Arrival Thresholds," Sustainability, MDPI, vol. 15(8), pages 1-19, April.
    11. Rapoport, Amnon & Mak, Vincent & Zwick, Rami, 2006. "Navigating congested networks with variable demand: Experimental evidence," Journal of Economic Psychology, Elsevier, vol. 27(5), pages 648-666, October.
    12. Zhao, Chunxue & Fu, Baibai & Wang, Tianming, 2014. "Braess paradox and robustness of traffic networks under stochastic user equilibrium," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 135-141.
    13. Yao, Jia & Huang, Wenhua & Chen, Anthony & Cheng, Zhanhong & An, Shi & Xu, Guangming, 2019. "Paradox links can improve system efficiency: An illustration in traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 35-49.
    14. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2018. "Stochastic user equilibrium with a bounded choice model," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 254-280.
    15. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    16. Rapoport, Amnon & Kugler, Tamar & Dugar, Subhasish & Gisches, Eyran J., 2009. "Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox," Games and Economic Behavior, Elsevier, vol. 65(2), pages 538-571, March.
    17. Eyran Gisches & Amnon Rapoport, 2012. "Degrading network capacity may improve performance: private versus public monitoring in the Braess Paradox," Theory and Decision, Springer, vol. 73(2), pages 267-293, August.
    18. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    19. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    20. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:67:y:2014:i:c:p:86-108. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.