A traveler-centric mobility game: Efficiency and stability under rationality and prospect theory

In this paper, we study a routing and travel-mode choice problem for mobility systems with a multimodal transportation network as a "mobility game" with coupled action sets. We formulate an atomic routing game to focus on the travelers' preferences and study the impact on the efficiency of the travelers' behavioral decision-making under rationality and prospect theory. To control the innate inefficiencies, we introduce a mobility "pricing mechanism," in which we model traffic congestion using linear cost functions while also considering the waiting times at different transport hubs. We show that the travelers' selfish actions lead to a pure-strategy Nash equilibrium. We then perform a Price of Anarchy and Price of Stability analysis to establish that the mobility system's inefficiencies remain relatively low and the social welfare at a NE remains close to the social optimum as the number of travelers increases. We deviate from the standard game-theoretic analysis of decision-making by extending our mobility game to capture the subjective behavior of travelers using prospect theory. Finally, we provide a detailed discussion of implementing our proposed mobility game.