Near-Optimal Equilibria I

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" summary

Gives a concrete toolbox that proves worst-case equilibrium efficiency via a lambda–mu smoothness inequality, then uses simple algebra and edge- or bidder-wise decomposition plus no-regret learning to extend pure-game bounds to Bayes‑Nash and time‑averaged play. Delivers specific guarantees: affine routing games ≤2.5 price of anarchy, first‑price auctions ≥50% (sharpenable to ~63%) of optimum, and shows the method applies across many games and priors.

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" chapters (17)

1. 0:00Intro
2. 1:35A Representative Result
3. 6:57The Price of Anarchy
4. 9:27What Do POA Bounds Look Like?
5. 14:33Canonical Example
6. 17:52Smooth Games
7. 19:54POA Bounds Without Convergence
8. 22:54A Hierarchy of Equilibria
9. 27:12No-Regret Sequences
10. 29:58Smooth = No-Regret Bound
11. 32:15Extension Theorems
12. 43:01Outline
13. 44:02Incomplete-Information Games
14. 45:27Example: First-Price Auction
15. 50:41POA with Incomplete Information: The Best-Case Scenario
16. 52:06Ideal Extension Theorem
17. 53:39Full Information