  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 the proposed
optimal contract can increase the SP's profit by 35%, comparing with the
conventional fixed monthly-period data plan.
