  We consider the problem of optimal charging of plug-in electric vehicles
(PEVs). We treat this problem as a multi-agent game, where vehicles/agents are
heterogeneous since they are subject to possibly different constraints. Under
the assumption that electricity price is affine in total demand, we show that,
for any finite number of heterogeneous agents, the PEV charging control game
admits a unique Nash equilibrium, which is the optimizer of an auxiliary
minimization program. We are also able to quantify the asymptotic behaviour of
the price of anarchy for this class of games. More precisely, we prove that if
the parameters defining the constraints of each vehicle are drawn randomly from
a given distribution, then, the value of the game converges almost surely to
the optimum of the cooperative problem counterpart as the number of agents
tends to infinity. In the case of a discrete probability distribution, we
provide a systematic way to abstract agents in homogeneous groups and show
that, as the number of agents tends to infinity, the value of the game tends to
a deterministic quantity.
