Brief Announcement: Effect of Strategic Grading and Early Offers in Matching Markets

Strategic suppression of grades, as well as early offers and contracts, are well-known phe-nomena in the matching process where graduating students apply to jobs or further education.In this paper, we consider a game theoretic model of these phenomena introduced by Ostrovskyand Schwarz, and study the loss in social welfare resulting from strategic behavior of the schools,employers, and students. We model grading of students as a game where schools suppress gradesin order to improve their students’ placements. We also consider the quality loss due to un-raveling of the matching market, the strategic behavior of students and employers in offeringearly contracts with the goal to improve the quality. Our goal is to evaluate if strategic gradingor unraveling of the market (or a combination of the two) can cause significant welfare losscompared to the optimal assignment of students to jobs. To measure welfare of the assignment,we assume that welfare resulting from a job – student pair is a separable and monotone functionof student ability and the quality of the jobs. Assuming uniform student quality distribution,we show that the quality loss from the above strategic manipulation is bounded by at most afactor of 2, and give improved bounds for some special cases of welfare functions. ∗[email protected], Dept of Computer Science, Cornell University. Supported in part by NSF grants CCF-0910940.†[email protected], Dept of Electrical Engineering and Computer Science, Massachusetts Institute ofTechnology. research was done while visiting Cornell university, supported by NSF grant CCF-0910940.‡[email protected], Dept of Computer Science, Cornell University. Supported in part by NSF grants CCF-0910940 and CCR-1215994), ONR grant N00014-08-1-0031, a Yahoo! Research Alliance Grant, and a Google ResearchGrant.arXiv:1507.02718v1[cs.GT]9Jul2015