Dynamic Game and Pricing for Data Sponsored 5G Systems With Memory Effect

By enabling revenue sharing between the network operators and the sponsors, the sponsored data has been proven to be a promising solution and is becoming a ubiquitous trend in the fifth generation (5G) networks for improving data connectivity for the users, increasing mobile engagement for the sponsors, and ensuring revenue for the network operators. In this paper, we investigate the data sponsored 5G system on a long-run basis. Compared with the conventional dynamic, i.e., long-run, model, the users in the system are memory-affecting, i.e., the users' decision-making is affected by their past service experience. In the system under our consideration, the users decide on the communication service access by jointly taking into account their instantaneous achievable utility and the history of their service experience, e.g., the past improved utility corresponding to the data sponsorship. The 5G system works as the utility provider for managing the communication service. Specifically, by using the concept of the power-law fading memory and the classical evolutionary game theory, we formulate a population game to model and study the dynamic behaviors of the players in the data sponsored 5G system. In the game, the interaction among the memory-affecting rational users is formulated as a fractional evolutionary game, and the communication service management of the 5G system is formulated as a classical evolutionary game. We analytically prove the existence and uniqueness of the solution to the population game. We both analytically and numerically verify the stability of the solution. The performance evaluation shows some insightful results. For example, the data sponsorship can significantly increase the data consumption for the users when they are heavily memory-affecting. Following this, we study a data sponsorship pricing problem with the objective to maximize the data consumption at the expense of the minimal data sponsorship.