Stackelberg Routing on Parallel Transportation Networks

Walid Krichene (), Jack D. Reilly (), Saurabh Amin () and Alexandre M. Bayen ()
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Walid Krichene: University of California at Berkeley
Jack D. Reilly: Google Inc. Mountain View
Saurabh Amin: MIT
Alexandre M. Bayen: University of California at Berkeley

Chapter 25 in Handbook of Dynamic Game Theory, 2018, pp 1107-1141 from Springer

Abstract: Abstract This chapter presents a game theoretic framework for studying Stackelberg routing games on parallel transportation networks. A new class of latency functions is introduced to model congestion due to the formation of physical queues, inspired from the fundamental diagram of traffic. For this new class, some results from the classical congestion games literature (in which latency is assumed to be a nondecreasing function of the flow) do not hold. A characterization of Nash equilibria is given, and it is shown, in particular, that there may exist multiple equilibria that have different total costs. A simple polynomial-time algorithm is provided, for computing the best Nash equilibrium, i.e., the one which achieves minimal total cost. In the Stackelberg routing game, a central authority (leader) is assumed to have control over a fraction of the flow on the network (compliant flow), and the remaining flow responds selfishly. The leader seeks to route the compliant flow in order to minimize the total cost. A simple Stackelberg strategy, the non-compliant first (NCF) strategy, is introduced, which can be computed in polynomial time, and it is shown to be optimal for this new class of latency on parallel networks. This work is applied to modeling and simulating congestion mitigation on transportation networks, in which a coordinator (traffic management agency) can choose to route a fraction of compliant drivers, while the rest of the drivers choose their routes selfishly.

Keywords: Transportation networks; Non-atomic routing game; Stackelberg routing game; Nash equilibrium; Fundamental diagram of traffic; Price of stability (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-44374-4_26

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