Spatial Equilibrium of V2G-Mobility Markets: A Mean Field Game Approach

Abstract

The integration of Vehicle-to-Grid (V2G) services into electric autonomous ride-sourcing fleets creates a fundamental trade-off between spatial displacement for mobility and temporal retention for energy arbitrage. This study investigates the stationary equilibrium of such large-scale fleets to analytically characterize the structural properties of the optimal fleet management strategy. We formulate a mean field game (MFG) framework under continuous energy constraints. We prove that the optimal policy exhibits a unique, spatially dependent threshold structure characterized by forced charging and V2G participation boundaries. To compute the equilibrium, we develop a Structure-Preserving Threshold Fictitious Play (SP-TFP) algorithm that ensures robust convergence by operating directly on the threshold manifold. Numerical results reveal that the equilibrium spontaneously organizes into Voronoi-like service cells. We further demonstrate that V2G infrastructure can either smooth spatial value disparities or exacerbate market polarization, depending on its deployment relative to demand hotspots. Ultimately, this study offers platform operators strategic insights into energy-spatial sorting and provides policymakers with actionable levers to enhance service equity and network robustness through targeted infrastructure planning.