课程信息

主题：Highlights from the History of Game Theory

时间：2024.12.23 (周一) 19:20-20:55

线下地址：六教6C300

主讲人：Yuval Peres | 北京雁栖湖应用数学研究院(Beijing Institute of Mathematical Sciences and Applications)

主办单位：清华大学求真书院

主讲人介绍

Yuval Peres obtained his PhD in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. Yuval has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored books on Markov chains, probability on graphs, game theory and Brownian motion. Dr. Peres is a recipient of the Rollo Davidson prize and the Loeve prize. He has mentored 21 PhD students. Dr. Peres was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, at the 2008 European congress of Math, and at the 2017 Math Congress of the Americas. In 2016, he was elected to the US National Academy of Science.

摘要

The concept of a zero sum game was introduced by Borel in 1921 and the crucial Minimax Theorem was proved by von Neumann in 1928. The best proof, found by Ville (1938) uses hyperplane separation. In 1944 the von Neumann - Morgenstern book "Games and economic behaviour" appeared. The next breakthrough was made by Nash (1950), who used the Kakutani and Brouwer fixed point theorems to show the existence of equilibria in general games. Key later developments I will survey include the theory of Stable matching by Gale and Shapley, the applications to adaptive learning by Blackwell, Shapley value for cooperative games, optimal auctions by Vickrey, Myerson and others (Auction theory is used millions of times every hour by search engines selling ads) , Evolutionary game theory by Maynard-Smith and Price (1973) , Games of incomplete information and correlated equilibria by Aumann. Recently game theory is being applied to PDE. It should be in the toolkit of every mathematician.