The Design and Analysis of a Mobility Game

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 hybrid action sets. The mobility resources (modes of transportation) may experience delays that grow with the aggregate utilization of the resource. We develop a theoretical framework based on repeated non-cooperative game theory for the travelers' routing and travel-mode choice within a general mobility system. This framework aims to study the behavioral impact of the travelers' decision-making on efficiency. We consider the traffic congestion and the waiting times at different transport hubs and introduce mobility monetary incentives as part of a pricing scheme. We show that the travelers' selfish behavior results in a Nash equilibrium, and then we perform a Price of Anarchy analysis to establish that the mobility system's inefficiencies remain relatively low as the number of travelers increases. We deviate from the standard game-theoretic analysis of decision-making by extending our modeling framework to capture the subjective behavior of travelers using prospect theory. Finally, we provide a simple example to showcase the effectiveness of our mobility game and incentives.