The Downs-Thomson Paradox with Endogenously Determined Departure Times

Abstract

We introduce a novel scenario that embeds the Downs-Thomson paradox in the context of departure-time choice during the morning commute. Commuters, departing from a common origin and traveling to a common destination, must choose between a congestible mode (car, road) and a non-congestible mode (train, railway). Those choosing the road must also select their departure times independently and anonymously. This decision involves a trade-off between the cost of queuing at the bottleneck and the cost of schedule delay (i.e., deviation from the desired arrival time). We numerically derive a symmetric mixed-strategy equilibrium that characterizes both mode and departure-time choices. We then examine how improvements to either the road or the railway affect mean travel costs. Our laboratory experiment shows that, consistent with the paradox, improving the railway lowers mean travel cost; however, contrary to the paradox, improving the road also reduces mean travel cost. These findings suggest that the Downs-Thomson paradox may fail to emerge fully when commuters must coordinate multiple strategic dimensions under intertemporal congestion externalities.