Mathematical Foundations of Game Theory

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).

• 1 Introduction.- 2 Zero-Sum Games: the Finite Case.- 3 Zero-Sum Games: the General Case.- 4 N-Player games: Rationality and Equilibria.- 5 Equilibrium Manifolds and Dynamics.- 6 Games in Extensive Form.- 7 Correlated Equilibria, Learning, Bayesian Equilibria.- 8 Introduction to Repeated Games.- 9 Solutions to the Exercises.- References.

“The book is a very valuable one and a nice piece of work in the area of game theory. … The book is enjoyable to read and truly an enrichment in game theory. It is widely well-structured and well-written and mathematically correct. … I recommend the book for researchers, graduate and undergraduate students who wants to get some insight in noncooperative game theory.” (Sirma Zeynep Alparslan-Gok, zbMATH 1426.91002, 2020)