PPT-6.896: Topics in Algorithmic Game Theory

Lecture 11 Constantinos Daskalakis Algorithms for Nash Equilibria Simplicial Approximation Algorithms Support Enumeration Algorithms Lipton Markakis Mehta Algorithms for Symmetric Games. Vazirani editors March 18 2009 Errata in 2nd Printing 2008 Chapter 14 Page 377 in the paragraph labeled Provide transit services only to customers change the sentence Therefore ASes should announce only customer routes to their providers and peers Lecture . 2. : . Myerson’s Lemma. Yang. . Cai. Sep 8,. . 2014. An overview of the class. Broad View: Mechanism. . Design. . and. . Auctions. First. . Price. . Auction. Second Price. /. Vickrey. Fall 2011. Constantinos Daskalakis. Lecture 11. Last. . Lecture. .... 0. n. Generic PPAD. Embed PPAD graph in [0,1]. 3. 3D-SPERNER. canonical . p. .w. . linear . BROUWER. multi-player. NASH. 4-player. Lecture 10. Constantinos Daskalakis. Last . Lecture. .... 0. n. Generic PPAD. Embed PPAD graph in [0,1]. 3. 3D-SPERNER. canonical . p. .w. . linear . BROUWER. multi-player. NASH. 4-player. NASH. 3-player. Lecture 7. Constantinos Daskalakis. Sperner’s. . Lemma. (. P. n. ): For all . i. ∈ {1,…, . n. }, none of the vertices on the face . x. i. = 0 uses color . i. ; moreover, color 0 is not used by any vertex on a face . Lecture 6. Constantinos Daskalakis. Sperner. ’ . s. Lemma in . n. dimensions. A. Canonical Triangulation of [0,1]. n. Triangulation. High-dimensional analog of triangle?. in 2 dimensions: a triangle. Fall 2011. Matt Weinberg. Lecture 24. Recap. Myerson’s Lemma: The Expected Revenue of any BIC Mechanism is exactly its Expected Virtual Surplus. Virtual Value . φ. (v): (defined on board). Virtual Surplus: The virtual valuation of the winner. Lecture 5: Myerson’s Optimal Auction. Yang. . Cai. Sep 17,. . 2014. An overview of . today’s class. Expected Revenue = Expected Virtual Welfare. 2 Uniform [0,1] Bidders Example. Optimal Auction. Lecture 12. Constantinos Daskalakis. The Lemke-. Howson. Algorithm. The Lemke-. Howson. Algorithm (1964). Problem:. Find an exact equilibrium of a 2-player game.. Since there exists a rational equilibrium this task is feasible.. Lecture 18. Constantinos Daskalakis. Overview. Social Choice Theory. Gibbard-Satterwaite. Theorem. Mechanisms with . Money (Intro). Vickrey’s. Second Price Auction. Mechanisms with Money (formal). Lecture 13. Constantinos Daskalakis. multiplayer zero-sum games. Multiplayer Zero-Sum, . wha. ?. Take an arbitrary two-player game, between Alice and Bob.. Add a third player, Eve, who does not affect Alice or Bob’s payoffs, but receives payoff. Fall 2016. Yang Cai. Lecture . 05. Overview so far. Recap:. Games, . rationality, . solution concepts. Existence Theorems for Nash equilibrium: . Nash’s theorem for general games (via . Brouwer. Author: . Neil . Bendle. Marketing Metrics Reference: Chapter 7. © 2014 Neil . Bendle. and Management by the Numbers, Inc.. Game Theory studies competitive and cooperative interactions.. Despite often using terms such as “players” and “games”, the ideas apply to markets and managers.. Lecture 8. Constantinos Daskalakis. 2 point Exercise. 5. . NASH . . BROUWER (cont.):. - Final Point:. We defined BROUWER for functions in the hypercube. But Nash’s function is defined on the product of .