Game Theory is a mathematical theory which studies strategic interactions among two or more decision makers. In other words, this young science studies situations in which rational agents make decisions to optimize their objectives. One goal of this course is to give students the mathematical tools to deal with an interactive problem. Game Theory, using mathematical tools, is important because it has numerous links to other disciplines including: Economics, Engineering, Political Science, Biology, Industrial and Medicine. These links provide incentives for interdisciplinary work and make such work invaluable. The interactive decision situations are called games, the agents (decision makers) are called players, their decisions are called strategies. Let us see some examples: if you drive a car in a busy street, you are playing a game with other drivers. When you make a bid at an auction, you are playing a game against the other bidders. Some years ago, in the United States, the design of the procedure by which the spectrum for telecommunications and cell phones for auctions was assigned to game theory experts.
Knowledge of the main models and solutions used in game theory. Capability to model real situations with these formal tools. Critical analysis of the assumptions of the theory and of its limits of applicability.
The object of the course is to give to students a deep understanding of tools in Game Theory
During the lessons we will work on the capability to identify a model to study via mathematical games.
Discussing problems via mathematical GT which will give us interesting and unusual solutions.
During the lessons we will work on the capability to identify models to study via games
At the end of the course, the students will be able to apply the strategic interaction models to real life and to think strategically.
Some modesl applied to Medicine and Environmental problems and studied via mathematical games will be studied and give us inusual solutions.
The courses of Mathematical Analysis 1 and 2
The lessons are in the room in presences and discussions of arguments. Teacher discuss with students problems and models of real life.
1. Introduction to Game Theory: what is a mathematical game? What is a strategic interaction?
2. From finite games to infinite ones
3. Solution for games: Nash equilibrium and efficiency of solution concept
4. Nash equilibrium in mixed strategies
5. Game in strategic form, in an extensive form, with complete information, with perfect information: examples
6. Games with potential (exact, ordinal, generalized etc)
7. Application to Economic models: oligfopoly problems, from static games (Cournot, Bertrand) to dynamic ones (Stackelberg)
8, Refinement of Nash equilibria: dominance, stability, evolutionary stable strategies
9. Games with hierarchic potential arising from a sequential situation with examples
10. Evolutionary stable equilibria, learning and the replicator dynamic: relationships
11. Cooperative games and solutions (Core, Shapley value et al)
12. From Vector Optimization to multicriteria games (both non cooperative or cooperative)
13. Solutions for multicriteria games and Pareto equilibria
14. Partially cooperative games and applications to environmental models
15. Application of GT to Medicin problems
1. Binmore K. "Fun and games: a text on Game theory", Lexington (Mass), D.C.Health 1993.
2. Branzei-Dimitrov-Tijs ''Models in cooperative game theory'', Springer, 2008
3. Costa G.-.Mori P. " Introduzione alla Teoria dei Giochi" ed. Il Mulino 1994
4. Ehrgott M., ''Multicriteria Optimization'' second edition, Springer-Berlin Heidelberg, 2005,
5. French S.,: '' Decision theory : an introduction to the mathematics of rationality'', New York : Ellis Horwood, 1993.
6. Fudenberg D., Tirole J., ''Game Theory'', The MIT Press, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1991.
7. Gonzalez-Diaz J., Garcia-Jurado I. and Fiestras-Janeiro M.G. "An introductory course on mathematical game theory". Graduate Studies in Mathematics 115. American Mathematical Society and Real Sociedad MatematicaEspanola. 2010.
8. Lucchetti R. ''Di duelli, scacchi, dilemmi. La teoria matematica dei giochi.'' Bruno Mondadori ed., 2001.
9. Maynard Smith J.,'' Evolution and the Theory of Games"Cambridge University Press, 1982.
10. Myerson, R. ''Game Theory: analysis of conflict'', Harvard: Harvard University Press, 1991.
11. Nasar S., ''Il genio dei numeri'', Rizzoli editore, 1999.
12. Owen G., ''Game Theory'' 2nd edition, Academic Press New York, 1982
13. Patrone F. ''Decisori razionali interagenti'' University Press, Pisa, 2007.
14. Peters H., ''Game Theory- A Multileveled Approach''. Springer, 2008.
15. Tijs S. " Introduction to Game Theory" Hindustan Book Agency,2003.
16. Vega Redondo F.,: ''Evolution Games and Economic Behaviour'', Oxford University Press, 1996.
17. Vincent T.L., Brown J.S.,: '' Evolutionary Game Theory, Natural Selection and Darwinian Dynamics'', Cambridge University Press, 2005.
18. Weibul J.W., '' Evolutionary Game Theory'' Cambridge:the MIT Press, 1995.
Ricevimento: For appointment contact by email: lucia.pusillo@unige.it
ANGELA LUCIA PUSILLO (President)
LINDA MADDALENA PONTA
SILVANO CINCOTTI (President Substitute)
https://corsi.unige.it/en/corsi/8734/studenti-orario
The exam is written, it is two hours long. We propone to students some mathematical models to study through mathematical Games as application of what we have seen at lesson. They must propose us a solution and discussing it. Each answer must be adeguately motivated.
During the course, the teacher wishes to know if students have well followed the lessons and learnt them. A way is to propose them a mathematical model to study via Game Theory. The students must discuss each other and propose a solution collaborating among themselves, making a team.
It is important for the students that they collaborate each other to learn to make a team and it is important for the teacher to understand which are the most difficult arguments.
