Fair ticket pricing in public transport as a constrained cost allocation game
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 linear and integer programming. The ticket pricing problem is considered to be a constrained cost allocation game, which is a generalization of cost allocation games that allows to deal with constraints on output prices and on the formation of coalitions. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that the fairness of prices can be improved substantially in this way.
KeywordsConstrained cost allocation games \(f\)-Nucleolus (f, r)-Least core Fair ticket prices
Mathematics Subject Classification90C90 91A80 91-08
We would like to thank three anonymous reviewers for their insightful comments on the paper. The work of Nam-Dũng Hoàng is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED).
- Borndörfer, R., & Hoang, N.-D. (2012). Determining fair ticket prices in public transport by solving a cost allocation problem. In H. G. Bock, X. P. Hoang, R. Rannacher, & J. P. Schlöder (Eds.), Modeling, simulation and optimization of complex processes (pp. 53–63). Berlin: Springer.CrossRefGoogle Scholar
- Borndörfer, R., Neumann, M., & Pfetsch, M. E. (2006). Optimal fares for public transport. In: Operations Research Proceedings 2005, pp. 591–596.Google Scholar
- Borndörfer, R., Neumann, M., & Pfetsch, M. E. (2008). Models for fare planning in public transport, Technical Report, ZIB Report 08–16, Zuse-Institut Berlin.Google Scholar
- Bussieck, M. R. (1998). Optimal lines in public rail transport, Ph.D. thesis. TU Braunschweig.Google Scholar
- Hallefjord, Å., Helming, R., & Jørnsten, K. (1995). Computing the nucleolus when the characteristic function is given implicitly: A constraint generation approach. International Journal of Game Theory, 24, 357–372.Google Scholar
- Hoang, N. D. (2010). Algorithmic cost allocation game: Theory and applications, Ph.D. thesis. TU Berlin.Google Scholar
- Young, H. P. (1994). Cost allocation. In R. J. Aumann & S. Hart (Eds.), Handbook of Game Theory (Vol. 2). Amsterdam: North-Holland.Google Scholar