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

The Dichotomous Affiliate Stable Matching Problem: Approval-Based Matching with Applicant-Employer Relations