We consider a network of prosumers involved in peer-to-peer energy exchanges, with differentiation price preferences on the trades with their neighbors, and we analyze two market designs: (i) a centralized market, used as a benchmark, where a global market operator optimizes the flows (trades) between the nodes, local demand and flexibility activation to maximize the system overall social welfare; (ii) a distributed peer-to-peer market design where prosumers in local energy communities optimize selfishly their trades, demand, and flexibility activation.We first characterize the solution of the peer-to-peer market as a Variational Equilibrium and prove that the set of Variational Equilibria coincides with the set of social welfare optimal solutions of market design (i). We give several results that help understanding the structure of the trades at an equilibrium or at the optimum. We characterize the impact of preferences on the network line congestion and renewable energy waste under both designs. We provide a reduced example for which we give the set of all possible generalized equilibria, which enables to give an approximation of the price of anarchy. We provide a more realistic example which relies on the IEEE 14-bus network, for which we can simulate the trades under different preference prices. Our analysis shows in particular that the preferences have a large impact on the structure of the trades, but that one equilibrium (variational) is optimal.

This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition and the individuals' common cost are all lower than in the corresponding nonatomic game (without coalitions). The individuals' cost is lower than the average cost to any coalition. Similarly, the average cost to a coalition is lower than that to any larger coalition. Whenever some members of a coalition become individuals, the individuals' payoff is increased. In the case of a unique coalition, both the average cost to the coalition and the individuals' cost are decreasing with respect to the size of the coalition. In a sequence of composite games, if a finite number of coalitions are fixed, while the size of the remaining coalitions goes to zero, the equilibria of these games converge to the equilibrium of a composite game played by the same fixed coalitions and the remaining individuals.1. At the CE, the average social cost, the individuals' cost and the average cost to each coalition are lower than the equilibrium cost at the WE of the corresponding nonatomic game.2. At the CE, the average cost to a coalition is lower than that to any other larger coalition. If a coalition sends flow on a certain arc, then any other larger coalition sends more on it. R

Device-to-device (D2D) content sharing, as a promising solution to rapidly growing mobile data traffic, is facing serious security issues. Hence, how to ensure its security is challenging and meaningful work. Covert communication is regarded as an emerging and cutting-edge security technique for its higher level of security and less need for channel state information (CSI), and accordingly, has attracted wide attention. However, it is not easy to directly apply covert communication to D2D content sharing to ensure both security and efficiency. In this paper, a novel covert communication model is constructed in D2D content sharing scenario, where the co-channel interference (CCI) introduced by spectrum reusing is exploited as the cover of contents so that the contents are hidden from the warden. Then, we propose a secure and efficient resource allocation scheme to ensure both security and efficiency of D2D content sharing by addressing the following two issues: 1) In order to guarantee the robustness of our scheme, covert constraints are learned by analyzing the detection performance at the warden, i.e., the security of D2D content sharing is guaranteed even considering some extremely adverse environments. 2) The joint spectrum allocation and power control is modeled as a two-sided matching problem and then reformulated as the one-to-one matching game based on the principle of mutual benefit, in order to ensure the quality of service (QoS) requirements of both D2D pairs and cellular users. Then, covert constraints guaranteed resource allocation algorithm based on Gale-Shapley algorithm is proposed. Its properties such as stability, optimality, convergence, and complexity are analyzed. The extensive simulation results are provided to verify the theoretical analyses and demonstrate the efficiency of our proposed algorithm, which has at least 7.63% performance gain compared with some existing approaches and no more than 4.83% performance loss compared with the exhaustive search. INDEX TERMS D2D content sharing, covert communication, co-channel interference, resource allocation, matching game.