The Influence of One Strategic Agent on The Matching Market
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Consider a matching problem with n men and n women, with preferences drawn uniformly from the possible (n!)^2n full ranking options. We analyze the influence of one strategic agent on the quality of the other agents' matchings in the Gale-Shapley Algorithm. We show that even though the Gale Shapley algorithm is famous for being optimal for men, one small change in the reported preferences is enough for the women to get a near optimal match. In this case, the quality of the matching dramatically improves from the women's perspective. The expected women-rank is O(^4(n)) and almost surely the average women-rank is O(^2+ϵ(n)) rather than a rank of O(n/(n)) in both cases under truthful regime.
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