MISES: Minimal Information Sufficiency for Effective Service

TL;DR

This paper analyzes category-based resource allocation mechanisms, establishing bounds on welfare and detection performance, and discusses the trade-offs in choosing category granularity for effective service coordination.

Contribution

It provides theoretical bounds and insights on the trade-offs in category-based mechanisms, including the sufficiency of demand-derived categories and entropy bounds for coordination.

Findings

Welfare gap bounds are tightly linked to within-category variance epsilon.

Demand-derived categories minimize welfare loss and misreporting incentives.

Finer categories improve welfare but worsen detection performance.

Abstract

Category-based coordination mechanisms allocate resources by mapping a declared service category to a fixed resource profile, without observing individual demand types. We establish three results for this class of mechanisms. First, the relative welfare gap Delta satisfies a tight two-sided bound in terms of the aggregate within-category allocation variance epsilon: (alpha/2W*)epsilon <= Delta <= (beta/2W*)epsilon. Second, the expected misreporting gain is bounded by the same epsilon without assumptions on agent strategy; demand-derived categories minimise both welfare loss and misreporting incentive simultaneously. Third, aggregate outcome metrics strictly dominate per-agent metrics for service-level detection under a homogeneity condition, for all parameter values, with a finite-sample power gap of O(1/m). At any fixed K, the demand-derived category label is the sufficient statistic for coordination: collecting per-agent data beyond the category label adds noise to the detection problem without reducing the welfare gap. However, welfare and detection impose structurally opposed demands on K: welfare improves with finer categories, detection worsens. The designer faces a feasibility band [Kmin, Kmax] and must choose K within it as a value judgement. We claim that any protocol achieving welfare gap Delta <= epsilon* and missed-detection rate <= beta* requires at least Hlb(epsilon*, beta*) bits of category entropy. We illustrate the mechanism on a synthetic population of 50,000 demand vectors and five weeks of production performance-management data from four anonymised operator networks (28,249 cells).