Computation of a Nash Equilibrium of Multiple-Leader Stackelberg Network Games

We propose a multiple-leader Stackelberg network game to model the pricing decisions of relay nodes on an arbitrary topology between a source and a destination, under a reservation-based traffic model. After deriving closed-form solutions for the special case of serial and parallel networks, we present a centralized algorithm that finds a Nash equilibrium of the multiple-leader Stackelberg network game. We design an algorithm that converges to a Nash equilibrium for an arbitrary relay topology. We analyze the performance of the algorithm in the context of energy-limited wireless networks.