DOCTORAL COURSE "GAME THEORY"
AUDIENCE. Doctoral students in mathematics, univeristy of Trento. Other interested doctoral students from other doctoral schools. Interested third year and laurea magistrale students are also welcome.
TEACHERS. Fabio Bagagiolo (University of Trento) and Dario Bauso (University of Palermo).
PERIOD. March-April 2013
FREQUENCY About four hours per week
TIMETABLE Wednesday and Thursday 15:30-17:30. Starting Wednesday March 6th, aula 7, entrance hall Povo 0.
SECOND LESSON: Thursday 7th March, 15:30, Aula Seminari di Matematica.
PROGRAM.Non-cooperative games, Pareto optimality, pure and mixed strategies, Nash equilibria, Stackelberg equilibrium. Cooperative games, imputation set, core, nucleolus. Stochastic games. Brouwer and Kakutani fixed point theorems. Optimal control problems, Pontryagin maximum principle, dynamic programming, Hamilton-Jacobi-Bellman equation, differential games, Isaacs equation. Large population optimal control problems, mean field games.
CONTACT Fabio Bagagiolo, email@example.com
PARTICIPANTS: : Daniele T., Giulia C., Matilde M., Riccardo L., Francesco C., Luca T., Anna B., Mariavittoria GdC., Emanuele B., Alessio M., Valentina C., Stefania O., Maurizio T., Margherita G., Jolanda W., Silvia L., Samuele, V.
- Suggested book: "A course in game theory" by Martin J. Osborne and Ariel Rubinstein (MIT Press, 1994), ISBN 0-262-65040-1
- The proof of the Brouwer fixed point theorem using Sperner and KKM can be found, for instance, in the book: Variational and Quasi-variational Inequalities, by Baiocchi and Capelo (it is just a small chapter inside a book of PDEs, variational inequalities and various applications).
- Lecture notes "Noncooperative Differential Games. A tutorial" by Prof. Alberto Bressan at his web-pageYou can also find a brief introduction to static noncooperative games and the proof of Cellina's lemma.
- Lecture notes "Viscosity solution of Hamilton-Jacobi equations and optimal control problems" by Prof. Alberto Bressan at his web-pageYou can also find the Pontryagin maximum principle, dynamic programming and several examples.
- A full treatement of the theory of viscosity solutions and its applications to optimal control problems can be found in the book "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations" by M. Bardi and I. Capuzzo Dolcetta, Birkhauser, 1997.
REGOLE PER L'ESAME. Al seguente link si trovano le regole per l'esame sia per i dottorandi che per gli studenti. Gli argomenti elencati, sotto forma di titoli di temi, sono quelli trattati durante il corso, e ovviamente, fanno riferimento a cio' che e' stato svolto in classe (piu' qualche esercizio suggerito).