Lectures Roberto Lucchetti (roberto.lucchetti at polimi dot it)
Goals The course is aimed at illustrating the fundamentals of the mathematical theory of interactions between agents. It starts with the discussion of the main assumptions underlying the theory, and it continues by considering the possible description of the games: the extensive and the strategic form. Both the cooperative and non cooperative theory will be considered. The goal is to explain how rationality can explain and/or predict and/or suggest the behavior of interacting agents. This is not limited to human being, it can also be applied to animals, networks of computers and so on.
Detailed description of the topics The main assumptions of the theory. Sulle ipotesi della teoria. Main differences between the decision thery and the interactive decision theory. Game theory at work, two classical and interesting examples: the bargaining problem, the matching problem. Games in estensive form. Combinatorial games. Zero sum games The Nash non cooperative model. Refinements of the concept of equilbrium. Strong and correlated equilibria. Some examples. Cooperative games, definitions, examples. Core, nucleolus, the Shapley value and power indices. This is the end of the 5 cfu part. For those taking 8 cfu: Social choice and Arrow’s theorem. Some complements of convex analysis.
Prerequisites Some mathematical Analysis and linear algebra.
Exams No midterms, possibility of an early evaluation after the end of the 5 cfu part (for all enrolled students, including 8 cfu) , written exam with exercises and two more theoretical questions. No oral part, unless very particular and motivated exceptions (it can be required either by the teacher or by the student, final decision by the teacher).
Bibliography R. Lucchetti, A primer in game theory, Esculapio, 2011 M. Maschler, E. Solan, S. Zamir, Game theory, Cambridge University Press, 2013