A Stackelberg game to optimize the distribution of controls in transportation networks

Please always quote using this URN: urn:nbn:de:0297-zib-14995
  • We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways.

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Author:Ralf Borndörfer, Bertrand Omont, Guillaume Sagnol, Elmar Swarat
Document Type:ZIB-Report
Tag:Controls in transportation networks; Polymatrix game; Stackelberg game
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Date of first Publication:2012/04/10
Series (Serial Number):ZIB-Report (12-15)
ISSN:1438-0064
Published in:A rev. vers. appeared in: Proceedings of the 3rd International Conference on Game Theory for Networks (GAMENETS 2012), volume 105 of Lecture Notes of the ICST, pp. 224 – 235, Vancouver, Canada, May 2012
DOI:http://dx.doi.org/10.1007/978-3-642-35582-0_17

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