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.


    Access

    Download


    Export, share and cite



    Title :

    Price of anarchy in electric vehicle charging control games: When Nash equilibria achieve social welfare



    Publication date :

    2018-01-01



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English


    Classification :

    DDC:    629



    On the connection between Nash equilibria and social optima in electric vehicle charging control games

    DEORI, LUCA / Margellos, Kostas / PRANDINI, MARIA | BASE | 2017

    Free access


    Interval methods for computing strong Nash equilibria of continuous games

    Kubica, Bartłomiej / Woźniak, Adam | BASE | 2016

    Free access

    On the existence of Nash equilibria in strategic search games

    Álvarez Faura, M. del Carme / Duch Brown, Amalia / Serna Iglesias, María José et al. | BASE | 2011

    Free access

    A simplicial algorithm approach to Nash equilibria in concave games

    Haake, Claus-Jochen / Su, Francis Edward | BASE | 2006

    Free access