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

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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.

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Acknowledgments

The authors extend their sincere thanks to the anonymous referees for their constructive comments. This study is jointly sponsored by the National Natural Science Foundation of China (71471014, 71401120) and the National Basic Research Program of China (2012CB725403-5).

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Authors and Affiliations

  1. MOE Key Laboratory of Urban Transportation Complex System Theory and Technology, Beijing Jiaotong University, Beijing, 100044, China

    Wen-yi Zhang

  2. School of Traffic and Transporation, Beijing Jiaotong University, Beijing, 100044, China

    Wei Guan & Ji-hui Ma

  3. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Jun-fang Tian

Authors
  1. Wen-yi Zhang
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  2. Wei Guan
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  3. Ji-hui Ma
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  4. Jun-fang Tian
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Correspondence to Wen-yi Zhang.

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Zhang, Wy., Guan, W., Ma, Jh. et al. A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game. Netw Spat Econ 15, 1075–1092 (2015). https://doi.org/10.1007/s11067-014-9281-3

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  • DOI: https://doi.org/10.1007/s11067-014-9281-3

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