Dynamic Stackelberg User-in-the-Loop Repeated Game for Device-to-Device Communications

This paper proposes a dynamic Stackelberg repeated game for decentralized Device-to-Device (D2D) communications overlaying cellular communications. The proposed game aims to jointly optimize D2D user behavior via a user-in-the-loop (UIL) approach; and minimize transmit power, while maximizing packet delivery ratio (PDR) for all D2D users. The Stackelberg game architecture consists of a single leader (base station BS) and multiple followers (D2D users), where the leader selects its satisfaction with the social welfare of the D2D users by considering the reaction of the followers from the charged price it assigns. The followers on the other hand select transmit power so as to guarantee a certain level of quality-of-experience (QoE) for all players. We express D2D user behavior as: (i) low data requirement; (ii) medium data requirement; and (iii) high data requirement. Therefore, each type of data requirement is assigned different utility functions due to the performance demands of D2D users. Both the leader and followers aim to maximize their utility function within the Stackelberg game. We prove that there exists an overall Stackelberg Equilibrium for our proposed game for all players, which is a sub-game perfect equilibrium, as the equilibrium achieved at each stage is independent of the game history. Our simulation results illustrate that once the leader rapidly converges to an optimal outcome with respect to satisfaction, the followers then rapidly converge to a Paretoefficient outcome with respect to transmit power and PDR. Keywords—D2D communications, dynamic Stackelberg game, power control, user-in-the-loop, quality-of-experience, Paretooptimality, Nash Equilibrium, wireless communications.