LP-Duality and the Cores of Games

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" summary

LP duality and complementary slackness drive three concrete results: a class of matching-based games with a full core characterization plus polynomial LPs that compute min-max fair, max-min fair and equitable core imputations; an extension of “core” beyond profit sharing to a noncooperative, game-against-nature model using total dual integrality; and a repair for general (nonbipartite) matching showing a constructive 2/3-approximate core when the exact core is empty.

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" chapters (15)

1. 0:00LP duality and game cores
2. 2:00Bondareva-Shapley Theorem
3. 4:53Tennis club profit sharing
4. 10:41Assignment game Shapley-Shubik
5. 13:35Core as profit sharing gold
6. 22:20Players who get profits
7. 25:35Stable matching lattices
8. 29:06Fair core imputations
9. 37:25Equitable core imputations
10. 38:32Shapley-Shubik theorem power
11. 40:22Total unimodularity in games
12. 41:27Flow games applications
13. 42:12Investment management game
14. 43:16Core beyond profit sharing
15. 44:20Q&A