Cost sharing rules face limits when customers hide time flexibility
Cost Sharing with Hidden Time Flexibility
Computer Science and Game Theory
Summary
When customers schedule services within certain time windows, companies can save costs by grouping overlapping requests. But if customers hide how flexible they really are, it can lead to unfair costs or inefficiencies. The authors show that when customers can misreport their availability from both sides, fair cost-sharing solutions only exist for up to three customers. However, if one endpoint of the time window is known and verified, fair sharing is possible for larger groups. Their results describe precisely when such cost-sharing rules can prevent customers from benefiting by hiding flexibility.
What this means in practice
- •For service schedulers: Design cost-sharing policies that prevent customers from hiding availability to unfairly lower payments when booking services.
- •For transportation planners: Improve grouping and billing rules for delivery or ride services where timing flexibility can be partially verified.
A theory result. No direct application yet.
Authors
Mohsen Pourpouneh, Farzaneh Rajabighamchi
Abstract
Customers often specify acceptable time intervals for receiving a service. When service on a date entails a fixed activation cost, overlapping intervals allow joint service and cost sharing. Customers may nevertheless conceal flexibility by reporting a smaller interval, affecting both operating cost and its allocation. We ask whether an operator can select a core allocation at every reported profile without making concealment profitable. We establish sharp population boundaries for preventing such coalitional reductions. When intervals may be narrowed from either end, a core-selecting rule preventing such reductions exists if and only if there are at most three customers. With four or more customers, impossibility holds even under Pareto contraction-proofness, which excludes deviations making every contracting customer weakly better off and at least one strictly better off. The impossibility persists when each contracting customer conceals only an arbitrarily small fraction of her feasible interval. The boundaries change when either the earliest or latest acceptable date of every customer is verifiable. With common verified dates, equal sharing is core-selecting and prevents such reductions for any population size. When verified dates may differ, the boundary rises to five: such a rule exists for up to five customers, whereas with six or more no core-selecting rule prevents the contracting customers from reducing their combined payment. Under Pareto contraction-proofness, however, core selection is possible for every population size on either one-sided domain. Finally, the relaxations needed for approximate core selection and coalitional contraction-proofness must grow with population size.