Cognitive Hierarchy in Day-to-Day Network Flow Dynamics

When making route decisions, travelers may engage in a certain degree of reasoning about what others will do in the upcoming day, rendering yesterday’s shortest routes less attractive. This phenomenon was manifested in a recent virtual experiment that mimicked travelers’ repeated daily trip-making process. Unfortunately, prevailing day-to-day traffic dynamic models failed to faithfully reproduce the collected flow evolution data therein. To this end, we propose a day-to-day traffic behavior modeling framework based on the cognitive hierarchy theory, in which travelers with different levels of strategic reasoning capabilities form their own beliefs about lower step travelers’ capabilities when choosing their routes. Two widely studied day-to-day models, the network tatonnement process dynamic and the logit dynamic, are extended into the framework and studied as examples. Calibration of the virtual experiment is performed using the extended network tatonnement process dynamic, which fits the experimental data reasonably well. Our analysis reveals that both extended dynamics exhibit multiple equilibria, one of which corresponds to the classic user equilibrium. We further analyze and characterize these nonuser equilibrium states. Whereas analyzing global stability is intractable because of the presence of multiple equilibria, local stability criteria near equilibria are developed analytically. General insights on how key parameters affect the stability of user equilibria are unveiled.