A Stackelberg Game to Optimize the Distribution of Controls in Transportation Networks

Ralf Borndörfer; Bertrand Omont; Guillaume Sagnol; Elmar Swarat

Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers

Research Article

A Stackelberg Game to Optimize the Distribution of Controls in Transportation Networks

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@INPROCEEDINGS{10.1007/978-3-642-35582-0_17,
    author={Ralf Bornd\o{}rfer and Bertrand Omont and Guillaume Sagnol and Elmar Swarat},
    title={A Stackelberg Game to Optimize the Distribution of Controls in Transportation Networks},
    proceedings={Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers},
    proceedings_a={GAMENETS},
    year={2012},
    month={12},
    keywords={Stackelberg game Polymatrix game Controls in transportation networks},
    doi={10.1007/978-3-642-35582-0_17}
}

Ralf Borndörfer
Bertrand Omont
Guillaume Sagnol
Elmar Swarat
Year: 2012
A Stackelberg Game to Optimize the Distribution of Controls in Transportation Networks
GAMENETS
Springer
DOI: 10.1007/978-3-642-35582-0_17

Ralf Borndörfer¹^,*, Bertrand Omont²^,*, Guillaume Sagnol¹^,*, Elmar Swarat¹^,*

1: ZIB (Zuse Institut Berlin)
2: Ecole Centrale Paris

*Contact email: borndoerfer@zib.de, bertrand.omont@student.ecp.fr, sagnol@zib.de, swarat@zib.de

Abstract

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 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.

Keywords: Stackelberg game Polymatrix game Controls in transportation networks

Published: 2012-12-11

: http://dx.doi.org/10.1007/978-3-642-35582-0_17