[Paper Review] A Novel Mobile Data Contract Design with Time Flexibility

Yi Wei, Junlin Yu+2 more|arXiv (Cornell University)|Jun 19, 2018

Digital Platforms and EconomicsBusiness, Management and Accounting22 references4 citations

TL;DR

This paper proposes a novel mobile data contract design that offers time-flexible data plans with variable period lengths (e.g., monthly, six-monthly, yearly) to better match heterogeneous consumer demand patterns. Using contract theory, it designs incentive-compatible and individually rational period-price contracts for both discrete and continuous consumer-type models, achieving up to a 37% increase in service provider profit compared to conventional one-month plans.

ABSTRACT

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.

Motivation & Objective

• Address the inefficiency of fixed monthly data plans that fail to accommodate fluctuating user data demands across periods.
• Design a time-flexible data contract that allows users to choose plans with varying period lengths to reduce utility loss from unused or overused data.
• Maximize the service provider’s expected profit under information asymmetry, where consumer types (data demand variability) are private information.
• Develop a practical contract mechanism for continuous consumer types by grouping users and assigning period-price pairs to each group.
• Ensure truthful revelation of consumer types through incentive compatibility (IC) and individual rationality (IR) constraints in the contract design.

Proposed method

• Formulate a contract-theoretic framework where the service provider offers a menu of period-price combinations to elicit truthful consumer type revelation.
• For discrete consumer types, assign one period-price pair per type, ensuring IC and IR constraints are satisfied for each type.
• For continuous consumer types, partition users into finite groups based on demand variability (σ), then assign a single period-price pair per group.
• Use an iterative algorithm to jointly optimize group boundaries and period assignments, maximizing the SP’s profit under IC and IR constraints.
• Leverage the IP property (increasing differences in valuation) to ensure higher-type users receive longer periods and higher prices, improving contract efficiency.
• Apply numerical optimization to evaluate profit gains across different distributions (uniform, exponential, truncated normal) and group counts.

Experimental results

Research questions

• RQ1 How can a mobile service provider design a data contract with variable period lengths to better serve consumers with heterogeneous data demand patterns across time?
• RQ2 What are the necessary and sufficient conditions for a feasible contract that ensures consumers truthfully reveal their private demand types?
• RQ3 How does the profit of the service provider compare between fixed monthly plans, existing rollover plans, and the proposed time-flexible contract?
• RQ4 What is the optimal number of contract items (period-price pairs) in a continuous consumer-type model to balance profit gains and operational complexity?
• RQ5 How does the structure of the contract (grouping strategy and period assignment) affect the SP’s ability to extract surplus from different consumer segments?

Key findings

• The proposed optimal contract increases the service provider’s profit by up to 37% compared to a conventional one-month data plan under a uniform consumer type distribution.
• Compared to the existing two-month rollover plan, the proposed contract increases profit by 21% under uniform, 61% under exponential, and 26% under truncated normal distributions.
• Profit increases with the number of groups in the continuous model, but the marginal gain diminishes significantly beyond four groups, with 4-group contracts achieving over 98% of the profit of 6-group contracts.
• The 4-group contract is identified as a practical and efficient choice, balancing profit maximization and operational simplicity, aligning with real-world contract designs.
• The IP property ensures that longer periods are optimally assigned to higher-variability (higher-type) users, enabling better surplus extraction and improved contract efficiency.
• The iterative algorithm for group boundary and period assignment converges to a sub-optimal solution that significantly outperforms standard fixed-period plans in profitability.