A dynamic population game model of non-monetary bottleneck congestion management under elastic demand using karma

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 trade-off 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.