A Game Theoretic Model of Road Usage

Abstract

This paper explores the use of the theory of games as a tool for modelling road usage decisions. By explicitly considering the interdependence among road users and their ‘payoffs’ (utility) from road use, an adapted symmetric form of the ‘game of chicken’ is developed. The paper explores the various possible equilibria in this game. The mixed strategy symmetric Nash equilibrium is derived and a probability of road usage by a single user is calculated from this. The latter depends explicitly upon the generalised costs of road usage that include both the monetary and time costs of travel. From the single road user probability of usage, measures of the expected number of users are derived. An examination is made of how these vary with variations in the level of the generalised cost of usage. This provides an insight into how the tools of game theory may aid the understanding of the generation and regulation of road congestion.

Citation

James, T. (1998), "A Game Theoretic Model of Road Usage", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 401-409. https://doi.org/10.1108/9780585474182-039