Mobile Data Offloading with Flexible Pricing

We consider a data offloading scenario where the small-cell service providers (SSPs) are allowed to implement a flexible-pricing scheme. In the aforementioned scheme, the price that an SSP charges the mobile-network operator (MNO) depends on the amount of MNO's traffic that is offloaded onto the respective SSP. Formulating the SSPs' problem of determining their traffic-dependent prices as a Bayesian game, we first show that there exists no Nash equilibriums in pure strategies. We then proceed to derive the structure of a mixed-strategy symmetric Bayesian Nash equilibrium (BNE). We also compare the flexible-pricing scheme with the traditional flat-pricing scheme (where the SSPs are restricted to announce a single price, irrespective of the traffic that is offloaded onto them) in terms of the payoffs achieved by the SSPs as well as the MNO. We show that the SSPs benefit under the flexible-pricing scheme while the MNO incurs a loss in payoff; however, the net-payoff of the system remains balanced. Formally, in terms of mechanism design, the flexible-pricing scheme is incentive compatible as all entities (including the neutral MNO) achieve a non-negative payoff. Finally, focussing on the SSPs' payoff, we conduct a numerical study to demonstrate the efficacy of the flexible-pricing scheme over the flat-pricing scheme (using price of anarchy as the metric).