A Study of an Atomic Mobility Game With Uncertainty Under Prospect Theory

In this paper, we present a study of a mobility game with uncertainty in the decision-making of travelers and incorporate prospect theory to model travel behavior. We formulate a mobility game that models how travelers distribute their traffic flows in a transportation network with splittable traffic, utilizing the Bureau of Public Roads function to establish the relationship between traffic flow and travel time cost. Given the inherent non-linearities and complexity introduced by the uncertainties, we propose a smooth approximation function to estimate the prospect-theoretic cost functions. As part of our analysis, we characterize the best-fit parameters and derive an upper bound for the error. We then show the existence of an equilibrium and its its best-possible approximation.