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The course aims at showing the main theoretical concepts of cooperative and noncooperative games together with the main algorithms for their analysis.
Nozioni di base di topologia. Convergenza in spazi metrici. Basic notions of topology.
Books by Robert Gibbons (Author of Game Theory for Applied Economists)
Convergence in metric spaces. Basic notions of probability and optimization. Classificazione dei giochi, legami con l’economia, limitazioni della teoria. Duopoli di Cournot e di Bertrand. Giochi non cooperativi in forma normale ed equilibri di Nash. Giochi di Stackelberg ed ottimizzazione bilivello.
Giochi sequenziali ad informazione completa e perfetta: Il problema della glochi, soluzione di Nash. Classification of games, connections wth economics, limitations of the theory.
Lotteries, preferences and utility functions. Cournot and Bertand duopolies.
Noncooperative games in normal form, Nash equilibria. Zero sum games, security strategies and minimax theorem. Mixed strategies, existence and uniqueness of equilibria. Dominace hiochi rationability, syncronous and asyncronous algorithms of iterated elimination. Noncooperative games via variational and Ky Fan inequalities, related algorithms.
Stackelberg games and bilevel optimization. Sequential games with complete and perfect information: Nash solution to the bargaining problem.
Cooperative games with transferable utility, classes of games and strategic equivalence, nucleous, nucleolous and Shapley value.
No textbook will be adopted. During the classes the instructor will provide a detailed list of references for each topic.
Some lecture notes by the instructor are available as well. The discussion focuses on the contents of the course and it is made of a sequence of questions in order to evaluate the level of understanding of giofhi topics.
The topic is chosen jointly by the student and the instructor.
Once the topic is agreed, the student has to deliver the report and the talk in at most 2 months. SID – Sistema informatico dipartimentale Direzione servizi informatici e amministrazione digitale Direzione Edilizia e Telecomunicazione.