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A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game

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  • Wen-yi Zhang
  • Wei Guan
  • Ji-hui Ma
  • Jun-fang Tian

Abstract

In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe the selfish rerouting evolutionary game. It is demonstrated that i) NPSD and PAP require the same amount of network information acquisition in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency under a plausible behavior description; iii) NPSD can maintain the solution invariance, which makes the trial and error process to identify a feasible step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is a rational behavior swapping process and the continuous-time NPSD is globally convergent. Using the day-to-day NPSD, a numerical example is conducted to explore the effects of the reaction sensitivity on traffic evolution and characterize the convergence of discrete-time NPSD. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:4:p:1075-1092
    DOI: 10.1007/s11067-014-9281-3
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    Cited by:

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    3. Watling, David P., 2016. "A route-swapping dynamical system and Lyapunov function for stochastic user equilibriumAuthor-Name: Smith, Michael J," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 132-141.
    4. Watling, David P. & Hazelton, Martin L., 2018. "Asymptotic approximations of transient behaviour for day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 90-105.
    5. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    6. Chai, Huajun, 2019. "Dynamic Traffic Routing and Adaptive Signal Control in a Connected Vehicles Environment," Institute of Transportation Studies, Working Paper Series qt9ng3z8vn, Institute of Transportation Studies, UC Davis.
    7. Dong-Fan Xie & Xiao-Mei Zhao, 2020. "Traffic Dynamics and Mode Choice’s Delay Effect Under Traffic Restriction in Two-Mode Networks," Networks and Spatial Economics, Springer, vol. 20(3), pages 873-913, September.
    8. Fangxia Zhao & Jianjun Wu & Huijun Sun & Ziyou Gao & Ronghui Liu, 2016. "Population-driven Urban Road Evolution Dynamic Model," Networks and Spatial Economics, Springer, vol. 16(4), pages 997-1018, December.
    9. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.

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