Routing Game with Nonseparable Costs for EV Driving and Charging Incentive Design

  • Benoît SohetEmail author
  • Olivier Beaude
  • Yezekael Hayel
Conference paper
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


Designing optimal incentive mechanisms for electric vehicles is an important challenge nowadays. In fact, this new type of vehicle influences several parts of society, at the transport level through congestion/pollution and at the energy level. In this paper, we consider the design of driving and charging optimal incentive through a routing game approach with multiple types of vehicles: gasoline and electric. We show that the game is not standard and needs a particular framework. We are able to prove the existence of a Wardrop equilibrium of this routing game with nonseparable costs, due to interaction through the energy cost. Our analysis is applied to a particular transportation network in which two paths are possible for vehicles, mainly one through the city center and another one outside. A fully characterization of Wardrop equilibrium is proposed, and optimal tolls are computed in order to minimize an environmental cost. Numerical results are provided on real data of electricity consumptions in France and in Texas, USA.


Congestion game Electric vehicle Nonseparable costs Wardrop equilibrium 


  1. 1.
    E. Altman and H. Kameda. Equilibria for multiclass routing problems in multi-agent networks. Dynamic Games and Applications, 7:343–367, 2005.MathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Brenna, M. Falvo, F. Foiadelli, L. Martirano, F. Massaro, D. Poli, and A. Vaccaro. Challenges in energy systems for the smart-cities of the future. In Energy Conference and Exhibition, 2012 IEEE International, pages 755–762, 2012.Google Scholar
  3. 3.
    C. Chau and K. Sim. The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands. Operations Research Letters, 31, 2003.MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Correa, A. Schulz, and N. Stier-Moses. A geometric approach to the price of anarchy in nonatomic congestion games. Games and Economic Behavior, 64:457–469, 2008.MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Dafermos. The traffic assignment problem for multiclass-user transportation networks. Transportation Science, 6(1):73–87, 1972.CrossRefGoogle Scholar
  6. 6.
    M. Florian and D. Hearn. Network equilibrium models and algorithms. Network routing, pages 485–550, 1995.Google Scholar
  7. 7.
    S. Han, S. Han, and K. Sezaki. Development of an optimal vehicle-to-grid aggregator for frequency regulation. IEEE Transactions on smart grid, 1(1):65–72, 2010.CrossRefGoogle Scholar
  8. 8.
    A. Ipakchi and F. Albuyeh. Grid of the future. IEEE power and energy magazine, 7(2):52–62, 2009.CrossRefGoogle Scholar
  9. 9.
    M. Jeihani, S. Lawe, and J. Connolly. Improving traffic assignment model using intersection delay function. 47th Annual Transportation Research Forum, New York, New York, March 23–25, 2006 208046, Mar. 2006.Google Scholar
  10. 10.
    N. Jiang and C. Xie. Computing and analysing mixed equilibrium network flows with gasoline and electric vehicles. Computer-aided civil and infrastructure engineering, 29(8):626–641, 2014.Google Scholar
  11. 11.
    L. Kleinrock. Queueing systems. Wiley Interscience, 1975.Google Scholar
  12. 12.
    A. Y. Lam, Y.-W. Leung, and X. Chu. Electric vehicle charging station placement: Formulation, complexity, and solutions. IEEE Transactions on Smart Grid, 5(6):2846–2856, 2014.CrossRefGoogle Scholar
  13. 13.
    A.-H. Mohsenian-Rad, V. W. Wong, J. Jatskevich, R. Schober, and A. Leon-Garcia. Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE transactions on Smart Grid, 1(3):320–331, 2010.CrossRefGoogle Scholar
  14. 14.
    B. of Public Roads. Traffic assignment manual. Technical report, U.S. Department of Commerce, Urban Planning Division; 1964.Google Scholar
  15. 15.
    M. Patriksson. The Traffic Assignment Problem: Models and Methods. Dover Publications, 2015.Google Scholar
  16. 16.
    G. Perakis. The price of anarchy when costs are non-separable and asymmetric. proccedings of IPCO, 2004.Google Scholar
  17. 17.
    T. Roughgarden and E. Tardos. How bad is selfish routing. in proceedings of FOCS, 2000.Google Scholar
  18. 18.
    Y. Sheffi. Urban transportation networks: Equilibrium analysis with mathematical programming methods. Prentice-Hall, Inc., 1985.Google Scholar
  19. 19.
    J. Tan and L. Wang. Real-time charging navigation of electric vehicles to fast charging stations: A hierarchical game approach. IEEE Transactions on Smart Grid, 8(2):846–856, 2017.Google Scholar
  20. 20.
    J. Wardrop. Some theoretical aspects of road traffic research. Proc Inst Civ Eng Part II, 1:325–278, 1952.Google Scholar
  21. 21.
    W. Wei, S. Mei, L. Wu, M. Shahidehpour, and Y. Fang. Optimal traffic-power flow in urban electrified transportation networks. IEEE Transactions on Smart Grid, 8(1):84–95, 2017.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.EDF Lab’, EDF R&D, OSIRIS DepartmentUniversity of Paris-SaclayPalaiseauFrance
  2. 2.LIA/CERI, University of AvignonAvignonFrance

Personalised recommendations