Recently, the mobile network operators (MNOs) are exploring more time flexibility with the rollover data plan, which allows the unused data from the previous month to be used in the current month. Motivated by this industry trend, we propose a general framework for designing and optimizing the mobile data plan with time flexibility. Such a framework includes the traditional data plan, two existing rollover data plans, and a new credit data plan as special cases. Under this framework, we formulate a monopoly MNO's optimal data plan design as a three-stage Stackelberg game: In Stage I, the MNO decides the data mechanism; In Stage II, the MNO further decides the corresponding data cap, subscription fee, and the per-unit fee; Finally in Stage III, users make subscription decisions based on their own characteristics. Through backward induction, we analytically characterize the MNO's profit-maximizing data plan and the corresponding users' subscriptions. Furthermore, we conduct a market survey to estimate the distribution of users' two-dimensional characteristics, and evaluate the performance of different data mechanisms using the real data. We find that a more time-flexible data mechanism increases MNO's profit and users' payoffs, hence improves the social welfare.Index Terms-Rollover data plan, Three-part tariff, Time flexibility, Game theory. ! •

The growing competition drives the mobile network operators (MNOs) to explore adding time flexibility to the traditional data plan, which consists of a monthly subscription fee, a data cap, and a per-unit fee for exceeding the data cap. The rollover data plan, which allows the unused data of the previous month to be used in the current month, provides the subscribers with the time flexibility. In this paper, we formulate two MNOs' market competition as a three-stage game, where the MNOs decide their data mechanisms (traditional or rollover) in Stage I and the pricing strategies in Stage II, and then users make their subscription decisions in Stage III. Different from the monopoly market where an MNO always prefers the rollover mechanism over the traditional plan in terms of profit, MNOs may adopt different data mechanisms at an equilibrium. Specifically, the high-QoS MNO would gradually abandon the rollover mechanism as its QoS advantage diminishes. Meanwhile, the low-QoS MNO would progressively upgrade to the rollover mechanism. The numerical results show that the market competition significantly limits MNOs' profits, but both MNOs obtain higher profits with the possible choice of the rollover data plan.

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Mobile Network Operators (MNOs) are providing more flexible wireless data services to attract subscribers and increase revenues. For example, the data trading market enables user-flexibility by allowing users to sell leftover data to or buy extra data from each other. The rollover mechanism enables time-flexibility by allowing a user to utilize his own leftover data from the previous month in the current month. In this paper, we investigate the economic viability of offering the data trading market together with the rollover mechanism, to gain a deeper understanding of the interrelationship between the userflexibility and the time-flexibility. We formulate the interactions between the MNO and mobile users as a multi-slot dynamic game. Specifically, in each time slot (e.g., every day), the MNO first determines the selling and buying prices with the goal of revenue maximization, then each user decides his trading action (by solving a dynamic programming problem) to maximize his long-term payoff. Due to the availability of monthly data rollover, a user's daily trading decision corresponds to a dynamic programming problem with two time scales (i.e., day-to-day and month-to-month). Our analysis reveals an optimal trading policy with a target interval structure, specified by a buy-up-to threshold and a sell-down-to threshold in each time slot. Moreover, we show that the rollover mechanism makes users sell less and buy more data given the same trading prices, hence it increases the total demand while decreasing the total supply in the data trading market. Finally, numerical results based on real-world data unveil that the time-flexible rollover mechanism plays a positive role in the user-flexible data trading market, increasing the MNO's revenue by 25% and all users' payoff by 17% on average.