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In this study, we analyse the global stability of the equilibrium in adeparture time choice problem using a game-theoretic approach that deals withatomic users. We first formulate the departure time choice problem as astrategic game in which atomic users select departure times to minimise theirtrip cost; we call this game the 'departure time choice game'. The concept ofthe epsilon-Nash equilibrium is introduced to ensure the existence ofpure-strategy equilibrium corresponding to the departure time choiceequilibrium in conventional fluid models. Then, we prove that the departuretime choice game is a weakly acyclic game. By analysing the convergent betterresponses, we clarify the mechanisms of global convergence to equilibrium. Thismeans that the epsilon-Nash equilibrium is achieved by sequential betterresponses of users, which are departure time changes to improve their ownutility, in an appropriate order. Specifically, the following behavioural rulesare important to ensure global convergence: (i) the adjustment of the departuretime of the first user departing from the origin to the correspondingequilibrium departure time and (ii) the fixation of users to their equilibriumdeparture times in order (starting with the earliest). Using convergencemechanisms, we construct evolutionary dynamics under which global stability isguaranteed. We also investigate the stable and unstable dynamics studied in theliterature based on convergence mechanisms, and gain insight into the factorsinfluencing the different stability results. Finally, numerical experiments areconducted to demonstrate the theoretical results.

Stability analysis of a departure time choice problem with atomic vehicle models