Annals of Operations Research

, Volume 226, Issue 1, pp 51–68 | Cite as

Fair ticket pricing in public transport as a constrained cost allocation game

  • Ralf Borndörfer
  • Nam-Dũng Hoang


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.


Constrained cost allocation games \(f\)-Nucleolus (f, r)-Least core  Fair ticket prices 

Mathematics Subject Classification

90C90 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).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Faculty of Mathematics, Mechanics, and InformaticsVietnam National UniversityHanoiVietnam

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