## 1 Introduction  
Due to the fast development of electric vehicle (EV) technology, optimal scheduling of EVs integration in the electricity trading floor is required. Several frameworks have been suggested to develop the decision-making of an EV aggregator in electricity markets [1; 2]. In [3], an optimization method for aggregator's participation in the day-ahead and secondary reserve is proposed. In [4] conditional value at risk (CVaR) is applied as a risk measurement in the decision-making process of a wind producer to confront the uncertainties in day-ahead (DA) and balancing markets. In [5], a stochastic model for energy and reserve scheduling considering risk management strategy is investigated. In [6], the impact of the market price and reserve market uncertainties via a stochastic programming structure is expressed to obtain the EV scheduling problem. Integrated scheduling of EVs and renewable resources in a microgrid is investigated in [7] in order to control the intermittency of renewable energy generations through the stored energy in EVs' batteries. Coordination of charging schedules of EVs with the objective of minimizing the total charging cost while considering varyingcharging power of EVs is proposed in [8]. An aggregator-based interactive charging management scheme adopting interruptible load pricing is investigated in [9] in which the EV aggregator will respond to the load control command of the grid. An economic framework of responsive load based on the elasticity factor is proposed in [10] to schedule the energy and reserve of a microgrid in the presence of renewable energy resources and EVs. In some of the related literature the optimization of the aggregator's expected profit is considered subject to the constraints related to the EVs' demand [11]. Authors in [12] propose a stochastic model in which the bidding strategy of an EV aggregator in DA and reserve markets is optimized without considering any risk aversion. In [13], a stochastic optimization problem for participation of plug-in EVs in electricity markets considering value at risk (VaR) as a measurement tool is investigated. A plug-in EV charging load is formulated in [14] to assess the influence of EVs on urban distribution networks. The authors in [15] tried to model the market price uncertainties to obtain fixed pricing, time-of-use pricing and real-time pricing by a retailer in a smart grid. In [16] a stochastic aggregated model of the EVs exchanging energy is formulated and the EVs' reaction to the stochastic balancing requests is presented. Also, the influence of vehicle-to-grid (V2G) service features of balancing contract is discussed. Optimal bidding strategies of EV aggregators in DA energy and ancillary services markets while considering renewable generation is proposed in [17] within a stochastic optimization model. Authors in [18] proposed a stochastic linear program for the participation of aggregator in DA and balancing markets while considering risk via CVaR terms and in [19] the authors discussed the effects of charging program of EVs on the grid. Since the EV aggregators can compensate the stochastic behavior of renewables or load forecasting errors, a cooperative game model has been presented in [20] to capture the interactions between utilities and parking lots in the spinning reserve market, considering the V2G scenario. EV aggregators could also form a non-cooperative game where they try to maximize their own profit in a competitive environment. Therefore, a given EV aggregator has difficulties making energy trading decisions and offering appropriate bids to the EV owners to make more profit. In this regard, a mathematical program with equilibrium constraints optimizing the aggregator's decisions is proposed in [21] to determine the optimal profit and to minimize the charging cost paid by the final customers. However, the work does not consider the performance of rival aggregators. In [22], in contrast to what is commonly assumed, the aggregator is supposed to affect market prices.