Abstract-In this paper, a new holistic distributed day-ahead energy management approach with desired equilibrium selection capability in a smart distribution grid is proposed. The interaction between customers and the distribution company is modeled as a single-leader multiplefollower Stackelberg game. The interaction among customers is modeled as a non-cooperative generalized Nash game because they meet a common constraint. Customers hold the average of the aggregate load in the appropriate domain to reshape it and improve the Load Factor.The strategy of the distribution company is day-ahead energy pricing obtained through maximizing its profit which is formulated as a stochastic conditional value at risk optimization to consider the uncertainty of the price of electricity in the wholesale market. Customers' strategies are based on hourly consumption of deferrable loads and scheduled charge/discharge rates of energy storage devices in response to price. It is proved that the generalized Nash game has multiple equilibria; hence, the distributed proximal Tikhonov regularization algorithm is proposed here to achieve the desired equilibrium. The simulation results validate the performance of the proposed algorithm with 31.46% increase in the Load Factor besides 45.89 % and 14.23 % reduction in the maximum aggregate demand and aggregate billing cost, respectively.