A novel mobile data contract design with time flexibility

In conventional mobile data plans, the data is associated with a fixed period (e.g., one month) and the unused data will be cleared at the end of each period. To take advantage of consumers' heterogeneous demands across different periods and meanwhile to provide more time flexibility, some mobile data service providers (SP) have offered data plans with different lengths of period. In this paper, we consider the data plan design problem for a single SP, who provides data plans with different lengths of period for consumers with different characteristics of data demands. We propose a contract-theoretic approach, wherein the SP offers a period-price data plan contract which consists of a set of period and price combinations, indicating the prices for data with different periods. We study the optimal data plan contract designs under two different models: discrete and continuous consumer-type models, depending on whether the consumer type is discrete or continuous. In the former model, each type of consumers are assigned with a specific period-price combination. In the latter model, the consumers are first categorized into a finite number of groups, and each group of consumers (possibly with different types) are assigned with a specific period-price combination. We systematically analyze the incentive compatibility (IC) constraint and individual rationality (IR) constraint, which ensure each consumer to choose the data plan with the period-price combination intended for his type. We further derive the optimal contract that maximizes the SP's expected profit, meanwhile satisfying the IC and IR constraints of consumers. Our numerical results show that our proposed optimal contract can increase the SP's profit over 35% comparing with the conventional monthly-period data plan.