Reserve System with Beneficiary-Share Guarantee

2025-11-25

AI Summary

This paper studies multi-class allocation under a minimum beneficiary share constraint—requiring the number of matches within a target group to constitute at least a prespecified fraction of total matches—to reconcile the inherent trade-off between fairness constraints and overall matching size. We develop a theoretical framework for the Pareto frontier based on minimal-cycle characterizations, establishing for the first time its concavity and monotonic decrease in marginal slope, and proving that the maximum matching loss relative to the unconstrained optimum is bounded by 50%. We design a polynomial-time solvable iterative Hungarian algorithm that efficiently generates the entire Pareto frontier. Furthermore, we characterize fundamental trade-offs between class prioritization and path independence in mechanism design. Our results provide a computationally tractable, interpretable theoretical foundation and algorithmic toolkit for designing and systematically evaluating fair allocation policies.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study allocation problems with reserve systems under minimum beneficiary-share guarantees, requirements that targeted matches constitute at least a specified percentage of total matches. While such mandates promote targeted matches, they inherently conflict with maximizing total matches. We characterize the complete non-domination frontier using minimal cycles, where each point represents an allocation that cannot increase targeted matches without sacrificing total matches. Our main results: (i) the frontier exhibits concave structure with monotonically decreasing slope, (ii) traversing from maximum targeted matches to maximum total matches reduces matches by at most half, (iii) the Repeated Hungarian Algorithm computes all frontier points in polynomial time, and (iv) mechanisms with beneficiary-share guarantees can respect category-dependent priority orderings but necessarily violate path-independence. These results enable rigorous evaluation of beneficiary-share policies across diverse allocation contexts.

Problem

• Reserve systems balance minimum beneficiary-share guarantees with maximizing total matches
• Characterize non-domination frontier using minimal cycles for allocation optimization
• Analyze trade-offs between targeted matches and total matches in allocations

Innovation

• Using minimal cycles to characterize non-domination frontier
• Repeated Hungarian Algorithm computes frontier points
• Mechanisms respect category-dependent priority orderings