While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach.

本文提出 Dichotomous Affiliate Stable Matching (DASM) 问题，通过权衡代理人和其关联方的接受或拒绝并基于加权估值函数来解决匹配市场偏好问题，通过人类研究和算法验证，证明该方法的高效性。

双半联盟稳定匹配问题：基于批准的申请者-雇主关系匹配