Offloading and Pricing Strategies for Heterogeneous Mobile Networks

Abstract

In this work we consider the joint problem of offloading and pricing in heterogeneous networks comprising two-tier operators, namely, a Mobile Network Operator (MNO) and a pair of competing Small-cell Service Providers (SSPs). The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offloading problem</i> involves the MNO deciding the amount of traffic that it wishes to offload onto the SSPs. The SSPs, in turn, interact with each other through a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pricing problem</i> that requires the SSPs to fix competitive prices so as to maximize their revenue by trading more offloaded data with the MNO. The nature of the pricing scheme – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">flexible</i> or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">flat</i> – is fixed by the regulators. In flexible-pricing the SSPs can charge the MNO differently for different amount of traffic flows offloaded onto them. In contrast, under the flat-pricing scheme the SSPs are restricted to announce a fixed price irrespective of the offloaded traffic. For both pricing schemes, the MNO’s offloading problem is first formulated as a Stackelberg game with MNO as the leader, while SSPs constitute the followers. The solution to the offloading problem is characterized in terms of Stackelberg equilibria, referred to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimal-offloading</i> strategy, which is in contrast to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">full-offloading</i> scenarios considered in the literature (where the entire data is naively offloaded onto the SSPs by the MNO). Next, the SSPs’ pricing problem (which appears as the followers’ game in the Stackelberg’s formulation) is formulated as a Bayesian game and the solution is characterized in terms of Bayesian Nash equilibria (BNE). We first establish that there are no BNEs in pure strategies, and then proceed to derive the structure of a mixed strategy symmetric BNE. Finally, we conduct an extensive numerical work to compare the performances of the flexible and flat-pricing schemes under optimal-offloading and full-offloading strategies. Through our study we find that the proposed optimal-offloading strategy yields a better payoff to the MNO, while the choice of pricing scheme (flexible or flat) that is favorable for the SSPs varies with the system parameters.