The morning commute bottleneck congestion problem has classically been modelled as a static game in which commuters act strategically based on their immediate Value of Time (VOT). This has restricted existing congestion mitigation techniques to rely on essentially monetary incentives to affect the static costs of the commuters. In contrast, a dynamic model enables characterizing the strategic tradeoff between immediate and future resource access rights and inspires the design of new classes of fair, non-monetary congestion mitigation schemes. In this paper, we show how the recently proposed Dynamic Population Game (DPG) framework can be leveraged to study a non-monetary economy for bottleneck congestion management based on karma, a non-tradable mobility credit. Our DPG model allows to consider an elastic demand of commuters that only travel if congestion is reduced, and we show that a Stationary Nash Equilibrium (SNE) is guaranteed to exist despite of the dynamic participation of these commuters. Through numerical case studies we illustrate how our tools can assist policy makers in taking informed decisions about complex policy outcomes. In particular, we show how the dynamic karma scheme is robust to a potentially detrimental rebound effect that would manifest in a static monetary scheme.

A popular remedy for the morning commute bottleneck congestion is to split the highway capacity into a managed lane that is kept in free-flow and a general purpose lane that is subject to congestion. A classical theoretical result is that the more capacity is allocated to the managed lane the less the resulting congestion. However, existing approaches to restrict access to the managed lane are primarily monetary, e.g., tolls, which severely limits the public willingness to accept them due to equity concerns. Following up on recent work which introduces karma as a completely non-monetary credit used to control access to a so-called Karma Priority (KP) lane, we first review the strategic problem of the commuters which is modeled as a dynamic population game. We then numerically investigate the effect of varying the KP lane capacity. The karma scheme is equitable with respect to different income classes irrespective of the capacity split, meanwhile achieving near-optimal traffic reduction. Thus, managing a larger fraction of the bottleneck could be more socially feasible under a karma scheme than a monetary scheme.