In this paper, we consider the problem that a group of plug-in electric vehicles (PEVs) seek to maximize their payoff by selecting a proper charging station and the charging stations try to maximize their revenue by adjusting the electricity price according to the total demands they received. Since both the decisions of the charging stations and the PEVs should be made dynamically under competition environments, we propose a two-level game framework to model this issue. At the lower level, the PEVs need to adapt their strategies, i.e. the charging station selection, according to the service they can get from each charging station, and we formulate it as an evolutionary game and use replicator dynamics to model the charging station selection process. Also, we propose an algorithm to arrive at the evolutionary equilibrium. At the upper level, each charging station needs to set the electricity price appropriately to maximize its revenue according to the received total amount of electricity requirement from PEVs. We formulate a differential game to describe the competition among the charging stations and analyze the Nash equilibrium for both open-loop strategies and closed-loop strategies. Simulation results demonstrate that the proposed mechanism can gain a higher profit and faster convergence speed than static control.
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