  Mobile data offloading is an emerging technology to avoid congestion in
cellular networks and improve the level of user satisfaction. In this paper, 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.
