Monotonicity in the trip scheduling problem

The equilibrium of the archetypal morning commute problem with α−β−γ preferences has been shown to be unstable with various rational adjustment mechanisms, under both continuous and discrete day-to-day dynamics. It is not clear however whether this result is general, or whether other variations of the trip scheduling problem may be stable. This paper focuses on the cost function and shows that it is monotone if and only if the marginal utility rate at destination is non-increasing with time. This implies that unlike the morning commute, the evening commute is stable in continuous time with various adjustment mechanisms. It also suggests (but does not prove) that the morning commute equilibrium is likely to be unstable also with many other schedule preferences and economically rational adjustment mechanisms. A simulation-based analysis illustrates these differences between the morning and evening commutes.