A distributed market framework for mobile data offloading

We develop a distributed market framework to price the offloading service, and conduct a detailed analysis of the incentives for offloading service providers and conflicts arising from the interactions of different participators. Specifically, we formulate a multi-leader multi-follower Stackelberg game (MLMF-SG) to model the interactions between the offloading service providers and the offloading service consumers in the considered market framework, and investigate the cases where the offloading capacity of APs is unlimited and limited, respectively. For the case without capacity limit, we decompose the followers' game of the MLMF-SG (FG-MLMF-SG) into a number of simple follower games (FGs), and prove the existence and uniqueness of the equilibrium of the FGs from which the existence and uniqueness of the FG-MLMF-SG also follows. For the leaders' game of the MLMF-SG, we also prove the existence and uniqueness of the equilibrium. For the case with capacity limit, by considering a symmetric strategy profile, we establish the existence and uniqueness of the equilibrium of the corresponding MLMF-SG, and present a distributed algorithm that allows the leaders to achieve the equilibrium. Finally, extensive numerical experiments demonstrate that the Stackelberg equilibrium is very close to the corresponding social optimum for both considered cases.