OVERVIEW

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. 

AIMS AND CONTENT

LEARNING OUTCOMES

Each result is proven and interpretated in an intuitive way to give to students the double aspect of mathematical tools and intuitive interpretation.

An adding goal of the course is to give to students  tools to study problems of real life and to evidence some new aspects of this young science.

AIMS AND LEARNING OUTCOMES

The objectif 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.

PREREQUISITES

The courses of Mathematical Analysis  1 and 2

TEACHING METHODS

The lessons are in the room in presences and discussions of arguments. Teacher discuss with students problems and models of real life.

SYLLABUS/CONTENT

1.Introduction to  Game Theory: what is a mathematical game? What is a strategic interaction ?

2. From finite gamaes 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, Refinment of Nash equilibria: dominance, stability, evolutionary stable strategies

9. Games with gerarchic 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

RECOMMENDED READING/BIBLIOGRAPHY

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.

TEACHERS AND EXAM BOARD

Exam Board

ANGELA LUCIA PUSILLO (President)

LINDA MADDALENA PONTA

LESSONS

LESSONS START

On Monday, 18th september 2023 at 2pm

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

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.

ASSESSMENT METHODS

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.

Exam schedule