A First Course on Zero-Sum Repeated Games
1st Edition
Published on 7. March 2002
Book
Paperback/Softback
XV, 204 pages
978-3-540-43028-5 (ISBN)
Description
The purpose of the book is to present the basic results in the theory of two-person zero-sum repeated games including stochastic games and repeated games with incomplete information. It underlines their relation through the operator approach and covers both asymptotic and uniform properties. The monograph is self-contained including presentation of incomplete information games, minmax theorems and approachability results. It is adressed to graduate students with no previous knowledge of the field.
Reviews / Votes
From the reviews:
"This book is an introduction to repeated zero-sum games, played in discrete time. It surveys the basic theory and recent developments, and definitely fills a gap. . The book emphasizes the links to convex analysis and to stochastic processes. It is primarily aimed at graduate students with no previous knowledge of the field, though it will clearly serve as a very useful reference book for experts in the field." (Nicolas Vieille, Mathematical Reviews, 2002 m)
"The book is a text book for graduate students or professional mathematicians on two-person, zero-sum, repeated games. . The book is . concisely written, has a substantial biography, and comes in a well bound soft cover edition. When a concept is first met in the text, it is highlighted in bold font: I found this to be a useful feature of the book. I recommend this book to any library collection in a university where there is an interest in game theory . ." (T. M. Mills, The Australian Mathematical Society Gazette, Vol. 30 (3), 2003)
More details
Series
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XV, 204 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 13 mm
Weight
347 gr
ISBN-13
978-3-540-43028-5 (9783540430285)
Schweitzer Classification
Person
Rida Laraki graduated from the École Polytechnique (Paris, France) in 1996 and did his PhD in mathematical game theory at the UPMC (University Pierre and Marie Curie). Since 2001, he is a researcher at the CNRS, affiliated with Lamsade (the computer science department of the University of Paris Dauphine-PSL). Since 2017, he is also a professor at the University of Liverpool (in the computer science department). He is responsible of the doctoral program in computer science at the University of Paris Dauphine, and was responsible of the french scientific society on the mathematics of optimization and decision: SMAI-MODE. He taught mathematical game theory over multiple years at several Grandes Écoles and Universities in France including École Polytechnique, ENSAE, ENSTA, ENS and UPMC. He is known for majority judgment, a new voting method based on game theory. His book with Michel Balinski on the subject was published by the MIT Press in 2011.
Jérôme Renault graduated in 1994 from ENSAE Paris and Université Paris 7 and received his PhD in 1998 from Cermsem, Université Paris 1 Panthéon-Sorbonne. He has been Maître de Conférences at Ceremade, Université Paris-Dauphine, held a game theory chair at École Polytechnique, and is since 2009 a math professor at Toulouse School of Economics, Université Toulouse 1 Capitole. He has been the head of the CNRS research group in Game Theory from 2012 to 2015, and has recently obtained a chair Game Theory and Artifical Intelligence within the new Toulouse institute ANITI. He contributes in particular to the theory of repeated games, stochastic games, games with signals, long-term dynamic programming, Markov decision processes and optimal control, strategic transmission of information and games with incomplete information.
Sylvain Sorin graduated in 1976 from the École Normale Supérieure de Saint Cloud and received his Doctorat d'État in 1981 from UPMC-Paris VI. He has been professor at Université L. Pasteur (Strasbourg ; 1985-1990), Université Paris X-Nanterre (1990-2000), and is currently at UPMC-Paris VI (now Sorbonne Université). He has given game theory courses in several institutions in France (ENA, ENSAE, École Polytechnique, ...) and was invited professor on several occasions, including at IMSSS (Stanford), Core (Louvain), IAS (Jerusalem), MSRI (Berkeley), IDS (Stony Brook), CRIDT (Jerusalem), IMPA (Rio), CMM (Santiago), CRM (Barcelona), and HIM (Bonn). His contributions include: supergames, stochastic and incomplete information games, merging and reputation, approachability, learning algorithms, stochastic approximation and game dynamics... He has been editor in chief of the International Journal of Game Theory and area editor for game theory for the journal Mathematics of Operations Research. He is a fellow of the Game Theory Society and of the Econometric Society. He gave the von Neumann lecture at the congress of the GTS (Maastricht, 2016). He is the co-author, with J.-F. Mertens and S. Zamir, of the book Repeated Games, Cambridge U.P. (2015).
Content
Introduction and Examples.- Games with Incomplete Information.- Repeated Games with Lack of Information on One Side.- Repeated Games with Lack of Information on Both Sides.- Stochastic Games.- Advances.- Minmax Theorems and Duality.- Approachability Theory.- Operators and Repeated Games.- Kuhn's Theorem for Repeated Games.