  In this paper, a static non-cooperative game formulation of the problem of
distributed charging in electrical vehicle (EV) networks is proposed. This
formulation allows one to model the interaction between several EV which are
connected to a common residential distribution transformer. Each EV aims at
choosing the time at which it starts charging its battery in order to minimize
an individual cost which is mainly related to the total power delivered by the
transformer, the location of the time interval over which the charging
operation is performed, and the charging duration needed for the considered EV
to have its battery fully recharged. As individual cost functions are assumed
to be memoryless, it is possible to show that the game of interest is always an
ordinal potential game. More precisely, both an atomic and nonatomic versions
of the charging game are considered. In both cases, equilibrium analysis is
conducted. In particular, important issues such as equilibrium uniqueness and
efficiency are tackled. Interestingly, both analytical and numerical results
show that the efficiency loss due to decentralization (e.g., when cost
functions such as distribution network Joule losses or life of residential
distribution transformers when no thermal inertia is assumed) induced by
charging is small and the corresponding "efficiency", a notion close to the
Price of Anarchy, tends to one when the number of EV increases.
