Stable Matching: Choosing Which Proposals to Make
Ishan Agarwal, Richard Cole

TL;DR
This paper analyzes why stable matching works well with short preference lists in large markets and proposes methods for agents to identify which proposals to include, improving efficiency while maintaining stability.
Contribution
It provides a new analysis showing that most agents can identify stable matches with short preference lists, extending results to various market sizes and settings, and introduces a new technique for analyzing the Deferred Acceptance algorithm.
Findings
Most agents have stable matches within O(log n) preferences.
Stable matchings yield similar utilities for nearly all agents in large markets.
Agents can identify stable matches with minimal proposals using an initial communication phase.
Abstract
To guarantee all agents are matched in general, the classic Deferred Acceptance algorithm needs complete preference lists. In practice, preference lists are short, yet stable matching still works well. This raises two questions: Why does it work well? Which proposals should agents include in their preference lists? We study these questions in a model, introduced by Lee [17], with preferences based on correlated cardinal utilities: these utilities are based on common public ratings of each agent together with individual private adjustments. Lee showed that for suitable utility functions, in large markets, with high probability, for most agents, all stable matchings yield similar valued utilities. By means of a new analysis, we strengthen Lee's result, showing that in large markets, with high probability, for but the agents with the lowest public…
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