  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.
