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In this paper, we present a study of a mobility game with uncertainty in thedecision-making of travelers and incorporate prospect theory to model travelbehavior. We formulate a mobility game that models how travelers distributetheir traffic flows in a transportation network with splittable traffic,utilizing the Bureau of Public Roads function to establish the relationshipbetween traffic flow and travel time cost. Given the inherent non-linearitiesand complexity introduced by the uncertainties, we propose a smoothapproximation function to estimate the prospect-theoretic cost functions. Aspart of our analysis, we characterize the best-fit parameters and derive anupper bound for the error. We then show the existence of an equilibrium and itsits best-possible approximation.

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