2017/03/13 by Jacky Lo, Mark C. Wilson, Lo, Jacky +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #91B68 #Algorithm #Artificial intelligence #Axiom #Axiomatic system #Complexity and Algorithms in Graphs #Computer Science and Game Theory (cs.GT) #Computer science #FOS: Computer and information sciences #Game Theory and Voting Systems #J.4 #Logic, Reasoning, and Knowledge #Matching (statistics) #Mathematical economics #Mathematical optimization #Mathematics #Probabilistic logic #Social choice theory #Sorting #acm:91B68 #cs.GT #msc:91B68
paper · pdf · doi:10.48550/arxiv.1703.04225
19 pages including several figures and appendix
arxiv created 2017/03/13 · openalex publication_date 2017/03/13 · arxiv updated 2017/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the Gale-Shapley algorithm; for one-sided matching, (random) Serial Dictatorship and Probabilistic Serial rule; for school choice, Gale-Shapley and the Boston mechanisms. The main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of efficiency and strategyproofness. However if we shift the focus to fairness, social welfare, tradeoffs between incompatible axioms, and average-case analysis, it is far from clear that these algorithms are optimal. We investigate new algorithms several of which have not appeared (to our knowledge) in the literature before. We give a unified presentation in which algorithms for 2-sided matching yield 1-sided matching algorithms in a systematic way. In addition to axiomatic properties, we investigate agent welfare using both theoretical and computational approaches. We find that some of the new algorithms are worthy of consideration for certain applications. In particular, when considering welfare under truthful preferences, some of the new algorithms outperform the classic ones.