Cooperative game theory; partition form games.
Repeated games.
Stochastic games: zero-sum games; competitive MDPs; evolutionary games with state process.
Mean field models: finite-state mean field model and examples; convergence to the mean field ODE; convergence for the stationary regime.
Mean field games: Static mean field games; examples and the convergence problem. Dynamics mean field games: model description of many player stochastic games of mean field type; examples; mean field game equilibrium; weak and strong equilibria; relaxed controls; convergence problem for open-loop strategies via the probabilistic approach; issues in the convergence problem for closed-loop strategies.
- *When we offer this course, we will choose a suitable subset from the above list of topics based on the requirements and interests of the students.
References:
Jerzy A. Filar and Okko Jan Vrieze, Competitive Markov Decision Processes. Springer Science & Business Media, 2012.
Lodewijk Kallenberg. Markov decision processes. Lecture Notes. University of Leiden 428, 2011.
R J Aumann, The core of a cooperative game without side payment, Transaction of the American Mathematical Society,1961.
Jean-François Mertens, Sylvain Sorin, and Shmuel Zamir, Repeated Games. Cambridge University Press, 2015.
R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications, Volume I and II, Springer 2019.
D. Lacker, Probabilistic compactification methods for stochastic optimal control and mean field games, Lecture Notes, 2018.
In addition, we will use relevant scientific publications.