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Algorithmic Game Theory

Algorithmic Game Theory. Instructor: Prof. Palash Dey, Department of Computer Science and Engineering, IIT Kharagpur. Game theory is the formal study of interaction between self-interested (or goal-oriented) systems (or agents or decision makers or players), and strategic scenarios that arise in such settings. It began life in Economics in the 1940's with the work of von Neumann and Morgenstern, but has since been applied to an extraordinary range of subjects, including political science, evolutionary biology and even to inspection regimes for arms control. Game theory has for years also played an important, if less recognized, role in several branches of computer science. Applications within computer science include the use of games in automated verification and model checking to model computing systems in an unknown and possibly adverse environment. In AI games are applied to the analysis of multi-agent systems. Recently, with the advent of the internet and e-commerce, many game theoretic questions in the interplay between economics and computing have received extensive attention. These include electronic auctions, and more generally mechanism design questions (inverse game theory) related to finding incentive structures for cooperation between independent entities on the internet. Wherever game theory plays a quantitative role, algorithmic and computational questions related to solving games are also of central importance. This course discusses algorithmic aspects of game-theoretic models, with a focus on recent algorithmic and mathematical developments. (from nptel.ac.in)

Lecture 58 - Stable Matching


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Lecture 01 - Introduction
Lecture 02 - Assumptions of Game Theory
Lecture 03 - Examples of Games
Lecture 04 - Equilibrium Concepts
Lecture 05 - Nash Equilibrium
Lecture 06 - Indifference Principle
Lecture 07 - Security of Players
Lecture 08 - Minmax Theorem
Lecture 09 - Implications of Minmax Theorem
Lecture 10 - MSNEs of Matrix Games
Lecture 11 - Iterative Eliminations of Dominated Strategies
Lecture 12 - Iterative Eliminations of Dominated Strategies (cont.)
Lecture 13 - Braess's Paradox
Lecture 14 - Yao's Lemma and its Applications
Lecture 15 - Support Enumeration Algorithm
Lecture 16 - Succinct Game
Lecture 17 - Potential Games
Lecture 18 - Best Response Dynamics
Lecture 19 - Fast Convergence of Best Response Dynamics
Lecture 20 - Computing ε-PSNE for Network Congestion Games
Lecture 21 - PSNE for Congestion Games
Lecture 22 - PSNE for Symmetric Congestion Games
Lecture 23 - Functional NP
Lecture 24 - PPAD Class
Lecture 25 - Sperner's Lemma
Lecture 26 - Approximate MSNE Computation
Lecture 27 - Correlated Equilibrium
Lecture 28 - Coarse Correlated Equilibrium
Lecture 29 - External Regret Framework
Lecture 30 - Multiplicative Weight Algorithm
Lecture 31 - Multiplicative Weight Algorithm (cont.)
Lecture 32 - Swap Regret and Correlated Equilibrium
Lecture 33 - Swap Regret to External Regret Reduction
Lecture 34 - Braess's Paradox and Pigou's Network
Lecture 35 - PoA of Selfish Routing Game
Lecture 36 - PoA of Selfish Load Balancing Game
Lecture 37 - Bayesian Game
Lecture 38 - BNE of First Price Auction
Lecture 39 - Extensive Form Game
Lecture 40 - Mechanism Design Intro
Lecture 41 - Implementation of Social Choice Functions
Lecture 42 - Revelation Principle
Lecture 43 - Properties of Social Choice Function
Lecture 44 - Gibbard-Satterthwaite Theorem
Lecture 45 - Quasilinear Environment
Lecture 46 - Ex-Post Efficiency
Lecture 47 - VCG Mechanism
Lecture 48 - Example of VCG Mechanism
Lecture 49 - Weighted VCG
Lecture 50 - Affine Maximizer
Lecture 51 - Recap of Topics Discussed So Far
Lecture 52 - Single Parameter Domain
Lecture 53 - DSIC in Single Parameter Domain
Lecture 54 - Mayerson's Lemma
Lecture 55 - Sponsored Search Auction
Lecture 56 - Intermediate Domain
Lecture 57 - Algorithmic Mechanism Design
Lecture 58 - Stable Matching
Lecture 59 - Gale-Shapley Algorithm
Lecture 60 - Properties of Stable Matching