This is a graduate-level game theory course designed for Ph.D. students in economics, finance and related fields. The goal of the course is two-fold: to endow students with the vocabulary, concepts and tools necessary to conduct research in wide range of applications of game theory, and to provide the students with a foundation for further research on game theory.
The course covers fundamental concepts of both cooperative and non-cooperative games. There are three textbooks that I find useful: A course in Game Theory by Osborne and Rubinstein, Game Theory by Fudenberg and Tirole and Game Theory: Analysis of Conflict by Roger B. Myerson.
The first part of the course covers the fundamental concepts in normal form games both under complete and incomplete information. We discuss all aspects of Nash equilibrium and Bayesian Nash equilibrium. Aside from existence results, after investing in topics such as "knowledge and information," we focus on the epistemic foundations of Nash equilibrium. We also discuss other equilibrium concepts such as proper equilibrium, correlated equilibrium, evolutionarily stable strategies etc.
The next part of the course focuses on sequential games---again under complete and incomplete information. We study a number of refinements of Nash equilibrium. This includes subgame perfect equilibrium, sequential equilibrium, perfect Bayesian equilibrium, trembling hand perfect equilibrium. We devote the rest of our time in this part on repeated games. We discuss basic folk theorems in the literature.
The last part of the course is on cooperative game theory. This part is based on Myerson's book. We delve into the differences and similarities of cooperative and non-cooperative approaches. First we work on axiomatic bargaining theory including Nash bargaining, Kalai-Smorodinsky, utilitarian and egalitarian bargaining solutions. Then we discuss stability (equilibrium) concepts such as stable set, core, Shapley's value and kernel in cooperative games.
Although, most of the lectures will be devoted to presentation of important concepts and tools of game theory, special topics such as, bargaining, reputation effects, learning, global games will also be discussed as time permits. The choice of special topics and applications will be determined based on students’ interest.
Bogachan Celen was a Columbia Business School faculty member from 2004 to 2014.