Bayesian Learning, Day-to-day Adjustment Process, and Stability of Wardrop Equilibrium

Abstract

In this study, we assume that drivers under day-to-day dynamic transportation circumstances choose routes based on Bayesian learning and develop a day-to-day dynamic model of network flow. This model reveals that a driver using Bayesian learning chooses the route that frequently takes the minimum travel time. Furthermore, we find that the equilibrium point of the day-to-day dynamic model is identical to Wardrop’s equilibrium. Under complete information (when information about which route takes the minimum travel time is given after the trips), Wardrop’s equilibrium is globally asymptotically stable and the day-to-day dynamic system converges to Wardrop’s equilibrium if initial recognition among drivers is distributed widely. Under incomplete information, Wardrop’s equilibrium is always globally asymptotically stable regardless of what the drivers’ initial recognition is. Paradoxically, the condition for stable equilibrium under incomplete information is more relaxed than that under complete information.