A Study of an Atomic Mobility Game With Uncertainty Under Prospect Theory
Ioannis Vasileios Chremos, Heeseung Bang, Aditya Dave, Viet-Anh Le, Andreas A. Malikopoulos
TL;DR
Overall, the paper addresses traveler decision-making under uncertainty in a directed mobility network by embedding prospect theory into an atomic splittable routing game with a common origin–destination pair. It combines Prelec's probability weighting $w(p)=\exp(-(-\log p)^{\\beta_3})$ and an S-shaped value function around the reference $c_e^0=c_e(f_e^{CRT})$ with edge costs given by the BPR form $c_e(f_e)=c_e^0\left(1+\frac{3}{20}\left(\frac{f_e}{f_e^{CRT}}\right)^4\right)$, and adopts a smooth approximation $\sigma(f_e)$ so that $c_i^{PT}(x)=\sum_{r_i}\sum_{e\in r_i}\sigma(f_e)$. It then proves the existence of a Nash equilibrium and derives an upper bound on the approximation error, enabling tractable analysis of mobility decisions under prospect-theoretic perception. The results offer a practical framework for congestion management and incentive design in future mobility systems where traveler behavior deviates from rationality.
Abstract
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.