Envy-free matchings with cost-controlled quotas
Girija Limaye, Meghana Nasre

TL;DR
This paper studies the problem of assigning agents to programs with resource-based quotas, focusing on envy-freeness and cost optimization, revealing complexity differences and providing approximation algorithms.
Contribution
It introduces the CCQ setting with cost-controlled quotas, analyzing the complexity of envy-free matchings for minimizing total and maximum costs, and offers approximation algorithms.
Findings
MINMAX is solvable in polynomial time.
MINSUM is NP-hard and hard to approximate.
LP-based approximation algorithms are developed for MINSUM.
Abstract
We consider the problem of assigning agents to programs in the presence of two-sided preferences, commonly known as the Hospital Residents problem. In the standard setting each program has a rigid upper-quota which cannot be violated. Motivated by applications where quotas are governed by resource availability, we propose and study the problem of computing optimal matchings with cost-controlled quotas -- denoted as the CCQ setting. In the CCQ setting we have a cost associated with every program which denotes the cost of matching a single agent to the program. Our goal is to compute a matching that matches all agents, respects the preference lists of agents and programs and is optimal with respect to the cost criteria. We consider envy-freeness as a notion of optimality and study two optimization problems with respect to the costs -- minimize the total cost (MINSUM) and minimize the…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Logic, Reasoning, and Knowledge
