72674 - TEORIA DEI GIOCHI

Conoscenze e abilità da conseguire

Al termine del corso, lo studente ha una conoscenza matematica dei fondamentali concetti e risultati che caratterizzano la teoria dei giochi, distinguendo fra i giochi strategici e quelli cooperativi che hanno importanti applicazioni in ambito informatico.

Contenuti

The course aims to provide discrete mathematics knowledge for understanding and interpreting problems arising in computer science. Especially in the second part, which is the main one, players are likely to become variables of objective functions (in combinatorial optimization problems), as well as coalitions may become clusters or feasible subsets in given set systems.

1 Strategic games

1.0 Rational preference (binary) relations: alternative representations and aggregation (Pareto efficiency)
1.1 Simultaneous move and multistage games
1.2 Extensive form, game tree and information sets 
1.3 Strategies: dominated, rationalizable and best responses
1.4 Random strategies and expected utility
1.5 Equilibrium: existence, multiplicity and efficiency
1.6 Coalitional strategies and strong equilibrium
1.7 Potential and congestion games

2 Cooperative games
2.1 Introduction to ordered structures: posets and lattices
2.2 Coalitional games and the Boolean lattice
2.3 Solutions: valuations and Moebius inversion; Pseudo-Boolean functions and polynomial multilinear extension
2.4 Probabilistic and random-order solutions
2.5 Shapley and Banzhaf solutions
2.6 Core and convexity
2.7 Cooperation restrictions: partitions, graphs and set systems
2.8 Coalition formation games
2.9 Coalition structures, games in partition function form

Testi/Bibliografia

Lecture notes are made periodically available to students. Many further readings, mostly in the form of journal articles, are specified during classes.

Metodi didattici

Lezioni frontali

Modalità di verifica e valutazione dell'apprendimento

Grades obtain through two written tests: one after the first half of the course (at end of october / beginning of november), and the other one as soon as classes end (around dec 20th). Occasionally, an additional oral discussion is necessary, in case the written tests display substantial ambiguities. The student may always ask to discuss his/her written tests.

Link ad altre eventuali informazioni

http://www.researchgate.net/profile/Giovanni_Rossi4

Orario di ricevimento

Consulta il sito web di Giovanni Rossi