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Problem 4. The Gale-Shapley Algorithm produces the unique M-optimal, W-pessimal stable matching. By falsifying her preference list, can a woman end up (after running the

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Problem 4. The Gale-Shapley Algorithm produces the unique M-optimal, W-pessimal stable matching. By falsifying her preference list, can a woman end up (after running the algorithm) with a better partner than she would with her true preference list? Give a proof or an example

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