PPT-1 Approximation in Algorithmic Game Theory

Robust Approximation Bounds for Equilibria and Auctions Tim Roughgarden Stanford University 2 Motivation Clearly many modern applications in CS involve autonomous selfinterested agents. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. Lecture 11. Constantinos Daskalakis. Algorithms for Nash . Equilibria. Simplicial. Approximation Algorithms. Support Enumeration Algorithms. Lipton-. Markakis. -Mehta. Algorithms for Symmetric Games. Princeton University. Game Theory Meets. Compressed Sensing. Based on joint work with:. Volkan. Cevher. Robert. Calderbank. Rob. Schapire. Compressed Sensing. Main tasks:. Design a . sensing . matrix. Sometimes we can handle NP problems with polynomial time algorithms which are guaranteed to return a solution within some specific bound of the optimal solution. within a constant . c. . of the optimal. 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.. Problem. Yan Lu. 2011-04-26. Klaus Jansen SODA 2009. CPSC669 Term Project—Paper Reading. 1. Problem Definition. 2. Approximation Scheme. 2.1 Instances with similar capacities. 2.2 General cases . Outline. Julia Chuzhoy. Toyota Technological Institute at Chicago. Routing Problems. Input. : Graph G, source-sink pairs (s. 1. ,t. 1. ),…,(. s. k. ,t. k. ).. Goal. : Route as many pairs as possible; minimize edge congestion.. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. How accurate is your estimate?. Differential Notation. The Linear Approximation to . y. = . f. (. x. ) is often written using the “differentials” . dx. and . dy. . In this notation, . dx. is used instead of . Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. When the best just isn’t possible. Jeff Chastine. Approximation Algorithms. Some NP-Complete problems are too important to ignore. Approaches:. If input small, run it anyway. Consider special cases that may run in polynomial time. Nima. . Namvar. PhD Student. Outline. Introduction. Matching . Games. Stackelberg. Games. Coalition Games. Future works. . Part1: . Introduction. Multi-agent Systems. Agent . capabilities:. Sensing the environment. 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.. Game theory . to analyze strategic behavior:. Given a strategic environment (a “game”), and an assumption about like behavior (e.g. Nash Equilibrium), we can predict what will happen.. Mechanism design .