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Erel Segal (talk | contribs) |
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The Gale–Shapley algorithm is a [[truthful mechanism]] from the point of view of the proposing side. This means that no proposer can get a better matching by misrepresenting their preferences. Moreover, the Gale–Shapley algorithm is even ''group-strategy proof'' for proposers, i.e., no coalition of proposers can coordinate a misrepresentation of their preferences such that all proposers in the coalition are strictly better-off.{{r|dubins-freedman}} However, it is possible for some coalition to misrepresent their preferences such that some proposers are better-off, and the others retain the same partner.{{r|huang}}
The Gale–Shapley algorithm is non-truthful for the non-proposing participants. Each may be able to misrepresent their preferences and get a better match.{{r|sisterhood}} However, successful misrepresentation requires knowledge of the other agents' preferences; without such knowledge, misrepresentation can make the agent worse-off. Moreover, even after the agent sees the final matching, he/she cannot deduce a strategy that would guarantee him/her a better outcome in hindsight. This makes
==Generalizations==
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