Determining Fair Ticket Prices in Public Transport by Solving a Cost Allocation Problem

  • Ralf Borndörfer
  • Nam-Dũng Hoàng
Conference paper


Ticket pricing in public transport usually takes a welfare maximization point of view. Such an approach, however, does not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that prices that are much fairer than standard ones can be computed in this way.


Public Transport Allocation Method Grand Coalition Cost Allocation Cooperative Game Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Borndörfer, M. Neumann, and M. E. Pfetsch, Optimal fares for public transport, Operations Research Proceedings 2005, (2006), pp. 591–596.Google Scholar
  2. 2.
    R. Borndörfer, M. Neumann, and M. E. Pfetsch,, Models for fare planning in public transport, Tech. Rep. ZIB Report 08-16, Zuse-Institut Berlin, 2008.Google Scholar
  3. 3.
    M. R. Bussieck, Optimal Lines in Public Rail Transport, PhD thesis, TU Braunschweig, 1998.Google Scholar
  4. 4.
    S. Engevall, M. Göthe-Lundgren, and P. Värbrand, The traveling salesman game: An application of cost allocation in a gas and oil company, Annals of Operations Research, 82 (1998), pp. 453–471.Google Scholar
  5. 5.
    D. Gately, Sharing the gains from regional cooperation: A game theoretic application to planning investment in electric power, International Economic Review, 15 (1974), pp. 195–208.Google Scholar
  6. 6.
    Å. Hallefjord, R. Helming, and K. Jèrnsten, Computing the nucleolus when the characteristic function is given implicitly: A constraint generation approach, International Journal of Game Theory, 24 (1995), pp. 357–372.Google Scholar
  7. 7.
    N. D. Hoang, Algorithmic Cost Allocation Game: Theory and Applications, PhD thesis, TU Berlin, 2010.Google Scholar
  8. 8.
    S. Littlechild and G. Thompson, Aircraft landing fees: A game theory approach, Bell Journal of Economics 8, (1977).Google Scholar
  9. 9.
    M. Maschler, B. Peleg, and L. S. Shapley, Geometric properties of the kernel, nucleolus, and related solution concepts, Mathematics of Operations Research, 4 (1979), pp. 303–338.Google Scholar
  10. 10.
    P. Straffin and J. Heaney, Game theory and the tennessee valley authority, International Journal of Game Theory, 10 (1981), pp. 35–43.Google Scholar
  11. 11.
    H. P. Young, Cost allocation, In R. J. Aumann and S. Hart, editors, Handbook of Game Theory, vol. 2, North-Holland, Amsterdam, 1994.Google Scholar
  12. 12.
    H. P. Young, N. Okada, and T. Hashimoto, Cost allocation in water resources development, Water Resources Research, 18 (1982), pp. 463–475.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Zuse Institute Berlin (ZIB)BerlinGermany

Personalised recommendations