  We study equilibria in an Electric Vehicle (EV) charging game, a cost
minimization game inherent to decentralized charging control strategy for EV
power demand management. In our model, each user optimizes its total cost which
is sum of direct power cost and the indirect dissatisfaction cost. We show
that, taking player specific price independent dissatisfaction cost in to
account, contrary to popular belief, herding only happens at lower EV uptake.
Moreover, this is true for both linear and logistic dissatisfaction functions.
We study the question of existence of price profiles to induce a desired
equilibrium. We define two types of equilibria, distributed and non-distributed
equilibria, and show that under logistic dissatisfaction, only non-distributed
equilibria are possible by feasibly setting prices. In linear case, both type
of equilibria are possible but price discrimination is necessary to induce
distributed equilibria. Finally, we show that in the case of symmetric EV
users, mediation cannot improve upon Nash equilibria.
