Effect of Strategic Grading and Early Offers in Matching Markets

TL;DR

This paper models how strategic grading suppression and early offers in matching markets can cause welfare loss, providing bounds on the extent of this loss and analyzing the impact of strategic behaviors on social welfare.

Contribution

It introduces a game theoretic model analyzing the welfare impact of strategic grading and early offers, with bounds on welfare loss under various conditions.

Findings

Welfare loss is bounded by a factor of 2 under uniform quality distribution.

Strategic behaviors can significantly reduce social welfare in matching markets.

Improved bounds are provided for specific welfare function cases.

Abstract

Strategic suppression of grades, as well as early offers and contracts, are well-known phenomena 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 Ostrovsky and 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 grades in order to improve their students' placements. We also consider the quality loss due to unraveling of the matching market, the strategic behavior of students and employers in offering early contracts with the goal to improve the quality. Our goal is to evaluate if strategic grading or unraveling of the market (or a combination of the two) can cause significant welfare loss compared 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 function of 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 a factor of 2, and give improved bounds for some special cases of welfare functions.