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In the reverse Stackelberg mechanism, by considering a decision function for the leader rather than a decision value in the conventional Stackelberg game, the leader can explore a wider decision space. This flexibility can result in realizing the globally optimal solution of the leader’s objective function, while controlling the reaction function of the followers, simultaneously. We consider an aggregator who purchases energy from the wholesale energy market. The aggregator acts as the leader for a group of plugged in electric vehicles (PEVs) and determines the price of energy versus consumption at each hour a day as its decision function. In the followers level, since the optimal charging strategies of the PEVs are coupled through the electricity price, the PEVs in a group are considered to cooperate in finding their Nash–Pareto-optimal charging strategy, by minimizing a social cost function. For a large number of PEVs, the cooperative cost minimization of PEVs can be modeled as a cooperative mean-field (MF) game. We propose a decentralized MF optimal control algorithm and prove that the algorithm converges to leader–follower MF $\varepsilon _{N}$ -Nash equilibrium point of the game. Furthermore, a decentralized reverse Stackelberg algorithm is implemented to achieve the optimal linear price function of the leader. Simulation results and comparison with benchmark methods are performed to demonstrate the advantages of the proposed method. Note to Practitioners—The effect of a large population of PEVs on the power grid such as overload and voltage drop is inevitable. Motivated by this, there are many research articles which propose different centralized and decentralized charging coordination solutions to address this problem. The core idea in the most of literature is: “How to IMPLEMENT a demand response (DR) program appropriately for charging coordination problem to avoid high peak load?” However, none of them propose a practical algorithm on “How to DESIGN a DR optimally by having limited information from the clients?” We propose a bilevel optimization algorithm to both design a DR program (i.e., price function) and also implement DR program to flatten the demand curve, accordingly. Another advantage of the proposed method is that the information structure of the problem is close to reality. There is no information exchange among the clients and also the utility company does not need to know the private information of the clients. The Utility Company only knows the charging profile of the PEVs in each day and broadcasts the price signal to the clients for the next day. The method is illustrated in an IEEE 5-bus system that supports our claims. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of energy consumption management of a large population of plug-in hybrid electric vehicles (PHEVs). A PHEV can be derived either on its gasoline or the battery modes while traveling, and can be either charged from or discharged to the grid while parking at home, respectively. This feature is the main novel consideration in our system model, besides taking into account the constraints like traveling time and distance, and the bounds on the charging power and state of charge of the battery. On the basis of the proposed model of PHEV, the optimal battery-gasoline energy management strategy is obtained in order to minimize the cost of energy and battery degradation for each user. Such a strategy can also compensate the peak load. Since the strategy of each PHEV affects other users’ cost through the electricity price, we model such an interaction as a game problem and we prove that there exist a unique Nash equilibrium point of the game. Then, due to the fact that the effect of a single PHEV of a large population on the other users’ costs is negligible, the theory of mean filed (MF) game is utilized to develop a decentralized control strategy for PHEVs. The lightweight information exchange of the proposed MF algorithm ensures a low computational cost and communication overhead. The proof of convergence for the proposed algorithm is given and it is shown that as the number of PHEVs goes to infinity the MF optimal strategy of the players converges to the unique Nash equilibrium point of the game. In simulation results, the effectiveness of the proposed method in terms of demand side management, peak shaving, convergence rate, and robustness is studied. [ABSTRACT FROM AUTHOR]

Device-to-device (D2D) communication has been recently proposed to reduce cellular traffic by directly connecting the local nodes. In this paper, we consider a cellular-based primary network coexisting with a cognitive D2D pair. The primary network consists of a base station and multiple cellular users, which can sell their spectrum to the D2D user. Additionally, under low-interference conditions, the spectrum can be simultaneously shared between cellular users and D2D-capable users, which is called the nonorthogonal sharing mode. We introduce a double-sided bandwidth-auction game for cognitive D2D communication. In the auction, the D2D transmitter has three types of service providers (SPs) or sharing modes. The SPs operate on different frequency spectra, and a D2D-capable pair intends to share these spectra. This situation is formulated as an auction game, where a D2D transmitter bids a demand price–bandwidth curve, and each SP offers a price–bandwidth supply curve. The Nash equilibrium point of the auction game is analytically obtained. Then, a learning method is proposed for the decision making of the players in an incomplete-information repeated game. Moreover, the convergence of the proposed learning method to the Nash equilibrium point is studied through the converse Lyapunov theorem. Finally, the proposed auction game is extended to the multiple-D2D case, and the optimal bandwidth allocation strategy to maximize the sum rate is derived. [ABSTRACT FROM PUBLISHER]

In an incomplete information game, a big challenge is to find the best way of exploiting available information for optimal decision making of the agents. In this paper, two decision making methods, namely model-based and learning-based bidding strategies, are proposed and compared, for repeated Cournot competition of the generators in a day-ahead electricity market. The sum of the rivals’ offered quantities (SROQ) is considered as the state of the agent and its value is estimated using an adaptive expectation method. In the model-based approach, the convergence of the agents’ strategies to the Nash equilibrium point is also studied in two different cases. In the learning-based approach, the optimal bidding strategy is learned through combination of state estimation and a reinforcement learning method. Using the estimated state (SROQ), the optimal decision is learned through a fuzzy Q-learning algorithm. Through a case study, which is performed on the three-bus benchmark Cournot model, the convergence of the generators’ bids to the Nash-Cournot equilibrium is examined. [ABSTRACT FROM AUTHOR]