Reward Optimization for Content Providers With Mobile Data Subsidization: A Hierarchical Game Approach

Mobile data subsidization launched by mobile network operators is a promising business model to provide economic benefits for the mobile data market and beyond. It allows content providers to partly subsidize mobile data consumption of mobile users in exchange for displaying a certain amount of advertisements. From a content provider perspective, it is of great interest to determine the optimal strategy for offering appropriate data subsidization (reward) in order to compete against others to earn more revenue and gain higher profit. In this paper, we take a hierarchical game approach to model the reward optimization process for the content providers. To analyze the relationship between the provider and the user, we first focus on the one-to-one interaction in a single-provider single-user system, and formulate a Mathematical Program with Equilibrium Constraints (MPEC). We apply the backward induction to solve the MPEC problem and prove the existence and uniqueness of the Stackelberg equilibrium. We then formulate an Equilibrium Program with Equilibrium Constraints (EPEC) to characterize the many-to-many interactions among multiple providers and multiple users. Considering the inherent high complexity of the EPEC problem, we utilize the distributed Alternating Direction Method of Multipliers (ADMM) algorithm to obtain the optimum solutions with fast-convergence and decomposition properties of ADMM.