  Electric vehicles (EVs) equipped with a bidirectional charger can provide
valuable grid services as mobile energy storage. However, proper financial
incentives need to be in place to enlist EV drivers to provide services to the
grid. In this paper, we consider two types of EV drivers who may be willing to
provide mobile storage service using their EVs: commuters taking a fixed route,
and on-demand EV drivers who receive incentives from a transportation network
company (TNC) and are willing to take any route. We model the behavior of each
type of driver using game theoretic methods, and characterize the Nash
equilibrium (NE) of an EV battery sharing game where each EV driver withdraws
power from the grid to charge its EV battery at the origin of a route, travels
from the origin to the destination, and then discharges power back to the grid
at the destination of the route. The driver earns a payoff that depends on the
participation of other drivers and power network conditions. We characterize
the NE in three situations: when there are only commuters, when there are only
on-demand TNC drivers, and when the two groups of drivers co-exist. In
particular, we show that the equilibrium outcome supports the social welfare in
each of these three cases.
