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Risk Aversion, Road Choice, and the One-Armed Bandit Problem

CERMICS, École des ponts Paris Tech, 77455 Marne la Vallée Cedex 2, France
CERMICS, École des ponts Paris Tech, 77455 Marne la Vallée Cedex 2, France
Université de Cergy-Pontoise, École des ponts Paris Tech, CORE, and Institut universitaire de France, France
jpc{at}cermics.enpc.fr
delara{at}cermics.enpc.fr
andre.depalma{at}eco.u-cergy.fr

This paper provides a theoretical analysis of advanced traveler information systems for road choice with risk-averse drivers who rationally learn over time, in a simple setting. For this purpose, we study the one-armed bandit problem where a driver selects, day after day, either a safe or a random road. Four information regimes are envisaged. The visionary driver knows beforehand, with certainty, the travel time on the random road, while the locally informed driver needs to select a road to acquire information on it. Two intermediary information regimes (fully and globally) are also envisaged. We analyze these four regimes and compare the optimal strategies and the individual benefits with respect to individual risk aversion. A numerical example also illustrates the impact of risk aversion on dynamic optimal strategies.

Key Words: traveler information systems; road choice; travel time uncertainty; risk aversion; bandit problem; expected utility theory
History: Received: July 2005; revised: July 2006; accepted: October 2006.