Prerequisite: Optimization Techniques (IE 601) or equivalent, and instructor's consent
Noncooperative game theory focusses on equilibrium in games, especially Nash equilibrium and it's refinements. It does not inform us when and why we might expect that the observed play in a game will correspond to one of these equilibria. In this course, we study these aspects. When a game is played again and again, equilibrium arises as the long-run outcome of a process. In this process, the players involved may not the fully rational. Thus this course aims to study various dynamic mechanisms whose long-run behaviour converges to the equilibrium. The following are the topics to be covered in this course.
- Refinements of Nash equilibrium
- Differential equations, inclusions and stochastic approximations
- Fictitious Play: Discrete time, continuous time and best reply dynamics
- Replicator dynamics, Evolutionary stable strategies
- Brown-Neumann-Nash dynamics
- Deterministic and stochastic evolutionary dynamics
- Approachability, Blackwell's theory
- Consistency, regret-based learning, smooth fictitious play
- Mean-field games
- N. Cesa-Bianchi and G. Lugosi, Prediction, Learning and Games, Cambridge University Press, 2006.
- E. Van Demme, Stability and Perfection of Nash Equilibria. Springer, 1991.
- D. Fudenberg and D.K. Levine, Theory of Learning in Games, M.I.T. Press, 1998.
- S. Hart and A. Mas-Collel, Simple Adaptive Strategies: From Regret-Matching to Uncoupled Dynamics, World Scientific, 2012.
- J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, 1998.
- W.H. Sandholm, Population Games and Evolutionary Dynamics, M.I.T. Press, 2010.
- K. Sigmund (Editor), Evolutionary Game Dynamics, AMS, 2011.
- P. Young, Strategic Learning and its Limits, Oxford, 2004.
- Several recent and relevant research and survey papers.