lec-5.pdf - Stable Marriage Problem Introduced by Gale and...

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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly.
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth).
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth). Original Problem Setting:
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth). Original Problem Setting: I Small town with n men and n women.
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth). Original Problem Setting: I Small town with n men and n women. I Each woman has a ranked preference list of men.
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth). Original Problem Setting: I Small town with n men and n women. I Each woman has a ranked preference list of men. I Each man has a ranked preference list of women.
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Stable Marriage Problem Introduced by Gale and Shapley in a 1962 paper in the American Mathematical Monthly. Proved useful in many settings, led eventually to 2012 Nobel Prize in Economics (to Shapley and Roth). Original Problem Setting: I Small town with n men and n women. I Each woman has a ranked preference list of men. I Each man has a ranked preference list of women. How should they be matched?
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What criteria to use?
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What criteria to use? I Maximize number of first choices.
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What criteria to use? I Maximize number of first choices. I Minimize difference between preference ranks.
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What criteria to use? I Maximize number of first choices. I Minimize difference between preference ranks. I Look for stable matchings
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Stability. Consider the couples: I Alice and Bob I Mary and John
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Stability. Consider the couples: I Alice and Bob I Mary and John Bob prefers Mary to Alice.
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Stability. Consider the couples: I Alice and Bob I Mary and John Bob prefers Mary to Alice. Mary prefers Bob to John.
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Stability. Consider the couples: I Alice and Bob I Mary and John Bob prefers Mary to Alice. Mary prefers Bob to John. Uh...oh! Unstable pairing.
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So.. Produce a pairing where there is no running off!
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So.. Produce a pairing where there is no running off! Definition: A pairing is disjoint set of n man-woman pairs.
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So..
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