The integration of energy systems such as electricity and gas grids and power and thermal grids can bring significant benefits in terms of system security, reliability, and reduced emissions. Another alternative coupling of sectors with large potential benefits is the power and transportation networks. This is primarily due to the increasing use of electric vehicles (EV) and their demand on the power grid. Besides, the production and operating costs of EVs and battery technologies are steadily decreasing, while tax credits for EV purchase and usage are being offered to users in developed countries. The power grid is also undergoing major upgrades and changes with the aim of ensuring environmentally sustainable grids. These factors influence our work. We present a new operating model for an integrated EV-grid system that incorporates a set of aggregators (owning a fleet of EVs) with partial access to the distribution grid. Then, the Cooperative Game Theory is used to model the behavior of the system. The Core is used to describe the stability of the interaction between these aggregators, and the Shapley value is used to assign costs to them. The results obtained show the benefit of cooperation, which could lead to an overall reduction in energy consumption, reduced operating costs for electric vehicles and the distribution grid, and, in some cases, the additional monetary budget available to reinforce the transmission and grid infrastructures.