A Game Theoretic Approach to the Determination of Hyperpaths in Transportation Networks

Jan-Dirk Schmöcker, Michael G.H. Bell, Fumitaka Kurauchi and Hiroshi Shimamoto
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Jan-Dirk Schmöcker: Tokyo Institute of Technology
Michael G.H. Bell: Imperial College London
Fumitaka Kurauchi: Gifu University
Hiroshi Shimamoto: Hiroshima University

Chapter Chapter 1 in Transportation and Traffic Theory 2009: Golden Jubilee, 2009, pp 1-18 from Springer

Abstract: Abstract In transit assignment, the common lines problem leads to the notion of a hyperpath, which is a set of paths that when used according to the “take whichever attractive line arrives next” strategy minimises the expected travel time. Similarly, the game theoretic approach to risk-averse traffic assignment leads to the generation of a set of paths which minimises expected travel time when a pessimistic assumption is made about on-trip events. The equivalence between the hyperpath of transit assignment and the set of paths generated by a multi-agent, zero sum game is shown in this paper. In particular, game theory is used to show that the path split probabilities proposed by Spiess and Florian (1989) are optimal for the risk-averse traveller who needs to make an on-the-spot decision between alternative routes. An alternative two-agent (single demon), zero-sum game is considered. The results of the multiple- and two-agent games are compared on a small example network, showing that the single demon game can lead to denser hyperpaths.

Keywords: Travel Time; Transportation Network; Route Choice; Transit Network; Transportation Research Part (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-1-4419-0820-9_1

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