Fairness in Repeated Matching: A Maximin Perspective
This addresses fairness in sequential matching for agents in allocation systems, though it is incremental with theoretical contributions.
The paper tackles the problem of repeatedly matching items to agents over multiple rounds to maximize the utility of the least advantaged agent, either overall or per round, and finds these problems computationally intractable but provides approximation algorithms and efficient solutions for special cases.
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least advantaged agent at the end of all rounds (optimal) or at the end of every individual round (anytime optimal). We investigate the computational challenges associated with finding (anytime) optimal outcomes and demonstrate that these problems are generally computationally intractable. However, we provide approximation algorithms, fixed-parameter tractable algorithms, and identify several special cases whereby the problem(s) can be solved efficiently. Along the way, we also establish characterizations of Pareto-optimal/maximum matchings, which may be of independent interest to works in matching theory and house allocation.