ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable
Introduce students to the main mathematical models for decision making in conflict situations, the main solutions provided from the different theories of rationality (in the case of non-cooperative conflicts) and justice (in the case of cooperative conflict ), the main methods of calculating these solutions, and the main applications of game theory.
STRATEGIC FORM GAMES (7 weeks-14 expository sessions).
Introduction to decision theory. Preferences and utility.
Introduction to strategic form games.
Examples: Cournot oligopoly and Bertrand oligopoly, auctions, etc .
Nash equilibrium in strategic form games. Nash Theorem.
Mixed strategies in finite games.
Bimatrix Games.
Two-person zero-sum games.
Matrix Games. Minimax theorem.
Introduction to the refinements of Nash equilibrium in finite games.
EXTENSIVE FORM GAMES (5 weeks-10 expository sessions).
Introduction to extensive form games.
Nash equilibrium in extensive form games. Kuhn 's Theorem.
Introduction to the refinements of Nash equilibrium in extensive form games.
An example: the Stackelberg duopoly.
MODELS OF BARGAINING (1 week-2 expository sessions).
Axiomatic approaches to bargaining problem.
Examples: a business negotiation, bankruptcy issues, etc.
Theorems of Nash and Kalai - Smorodinsky.
GAMES WITH UTILITY TRANSFER (1 week-2 expository sessions).
Introduction to games with transferable utility.
Examples: voting patterns, cost allocation, etc.
The core and the Shapley value. Bondareva - Shapley Theorem.
ACCESSORIES (work).
Other solution concepts, algorithms and calculation results.
Connections between cooperative and noncooperative games.
Game theory and operations research.
Applications of game theory.
Useful computer tools.
BASIC BIBLIOGRAPHY
B. Casas Méndez, G. Fiestras Janeiro, I. García Jurado and J. González Díaz (2012). "Introducción a la Teoría de Juegos''. USC Editora. Online: https://prelo.usc.es/Record/Xebook1-207
H. Peters (2015) "Game Theory". Ed. Springer.
Online: https://link.springer.com/book/10.1007%2F978-3-662-46950-7
COMPLEMENTARY BIBLIOGRAPHY
Books available in the faculty library:
R. Aumann and S. Hart (1992). "Handbook of Game Theory (Vol. 1)''. North-Holland.
R. Aumann and S. Hart (1994). "Handbook of Game Theory (Vol. 2)''. North-Holland.
R. Aumann and S. Hart (2002). "Handbook of Game Theory (Vol. 3)''. North-Holland.
J. M. Bilbao, F. R. Fernández (Eds.) (1999). "Avances en Teoría de Juegos con Aplicaciones Económicas y Sociales''. Publicaciones de la Universidad de Sevilla.
D. Blackwell and M.A. Girshick (1954). "Theory of Games and Statistical Decisions''. Wiley.
F. Carreras, A. Magaña, R. Amer (2001). "Teoría de Juegos''. Ediciones Universitat Politécnica de Catalunya.
M.D. Davis (1986). "Introducción a la Teoría de Juegos''. Alianza Universidad.
P. Dorman (2014). "Microeconomics''. Ed. Springer. Online:
https://link.springer.com/book/10.1007%2F978-3-642-37434-0
T. Driessen (1988). "Cooperative Games, Solutions and Applications''. Kluwer Academic Publishers.
J. W. Friedman (1986). "Teoría de Juegos con aplicaciones a la Economía". Alianza Universidad.
R. Gibbons (1992). "Un Primer Curso de Teoría de Juegos''. Antoni Bosch Editor.
F. J. Girón y M. A. Gómez Villegas (1977). "Teoría de los Juegos''. U.N.E.D.
J. González Díaz, I. García Jurado and G. Fiestras Janeiro (2010). "An Introductory Course on Mathematical Game Theory''. Graduate Studies in Mathematics, Vol. 115. American Mathematical Society and RSME.
T. Ichiishi (1983). "Game Theory for Economic Analysis''. Academic Press.
M. Kolmar (2017). "Principles of Microeconomics''. Ed. Springer. Online:
https://link.springer.com/book/10.1007%2F978-3-319-57589-6
R.D. Luce and H. Raiffa (1957). "Games and Decisions''. Wiley.
A. Mas-Colell, M.D. Whinston and J.R. Green (1995). "Microeconomic Theory''. Oxford University Press.
M. A. Mirás Calvo and E. Sánchez Rodríguez (2008). "Juegos Cooperativos con Utilidad Transferible usando MATLAB: TUGlab''. Servicio de Publicacións da Universidade de Vigo.
R. Myerson (1991). "Game Theory. Analysis of Conflict''. Harvard University Press.
M. Osborne and A. Rubinstein (1994). "A Course in Game Theory''. The MIT Press.
G. Owen (1995). "Game Theory''. Academic Press.
T. Parthasarathy and T.E.S. Raghavan (1971). "Some Topics in Two-Person Games''. Elsevier.
H. Peters (1992). "Axiomatic Bargaining Theory''. Kluwer Academic Publishers.
E. Sánchez and J. Vidal (2014). "Juegos Coalicionales". Servicio Publicaciones, UVigo.
S. Tijs (2003). "Introduction to Game Theory''. Hindustan Book Agency.
F. Trías de Bes (2020). "La solución Nash: La reactivación económica tras el COVID-19". Paidós.
E. van Damme (1991). "Stability and Perfection of Nash Equilibria''. Springer-Verlag. Online:
https://link-springer-com.ezbusc.usc.gal/book/10.1007/978-3-642-58242-4
J. von Neumann and O. Morgenstern (1947). "Theory of Games and Economic Behavior''. Princeton University Press. Online:
https://ebookcentral-proquest-com.ezbusc.usc.gal/lib/buscsp/detail.acti…
GENERAL AND SPECIFIC
Knowledge of the most important models, concepts and results of game theory.
Ability to model a multi-person decision problem as a game and analyze it using the methodologies of game theory.
Knowledge of the connections between game theory and social sciences (especially economics).
Ability to use this knowledge to analyze problems of competitive or cooperative interactions that arise in the field of
social sciences.
CROSS
Working in interdisciplinary teams, by incorporating abstraction and logical reasoning.
Read scientific texts both native tongue and other relevant in science, especially the English.
Students after taking this subject have deepened in the acquisition of the following skills in Mathematics: CG1, CG2, CG3, CG4, CG5, CE1, CE2, CE3, CE4, CE5, CE6, CE7, CE8, CE9, CT1, CT2, CT3, CT4 y CT5.
Expository and interactive classes (two of each type per week). In the interactive classes, students will be able to correct the proposed problems on the board.
Each student will have two hours of class in small groups in which they will present theoretical-practical material (individual or group work), complementary to that developed in the expository classes, which will also be delivered for correction.
Blackboard and video cannon will be used.
The usefulness of some online tools such as TUGlabWeb or different R libraries such as rgamer, CoopGame or powerindexR will be shown.
Student participation in class will be encouraged.
The relationship between game theory and the social sciences will be emphasized.
In the expository classes the CG1, CE1, CE2, CE3, CE4 and CT3 competences will be worked, mainly, while in the interactive seminary and laboratory classes, the CG3, CE5, CE6, CE7, CE8 competences will be done, respectively, and CT3 and CE8 and CE9. In the tutorials in very small groups we will work CG4 and CT3. Finally, for the non-contact hours dedicated to this subject, it is convenient to encourage the work of CG5, CT1, CT2 and CT5.
The expository and interactive teaching will be complemented with the virtual course of the subject, in which the students will find bibliographic materials. The tutorials will be in person or through MS-TEAMS or email.
Students will have two assessment systems at their disposal:
System 1: An exam of the subject that will consist of two parts. The first part will be on the theoretical aspects of the subject, it will be carried out without the help of material, will last 1.5 hours and will be worth 5 points. The second part will be on the practical part of the subject, will be carried out with the help of the notes and other material of the subject, will last 2.5 hours and will be worth 5 points.
System 2: It includes two ingredients:
2.1 Continuous assessment. It will consist of two tasks. The first one will be an individual exercise to be done outside class with a value of 2 points. The second task will be a group work to be carried out outside class, which includes the reading of a short document, the elaboration of a small report and the presentation to the teacher, with a value of 1.5 points.
2.2 Examination of the subject. Of the same characteristics as in system 1, and worth 3.25 points for each part of the exam.
System 3: It also includes two ingredients:
3.1 Continuous assessment. It will consist of three tasks. The first one will be an individual exercise of the non-cooperative games part to be done outside class with a value of 2 points. The second task will be a group work to be carried out outside class, including the reading of a short document, the elaboration of a short report and the presentation to the teacher, worth 1.5 points. The third one will be an individual exercise of the cooperative games part to be carried out outside class with a value of 1 point, involving the use of the computer tools shown in class, as well as data taken from real life.
3.2 Examination of the subject. Of the same characteristics as systems 1 and 2, and worth 2.75 points for each part of the exam.
For each system, the continuous evaluation assessments would be the same for all groups.
The student's final grade will be the maximum of those obtained by each of the two systems explained above. In order to pass the subject, it is necessary to achieve at least 5 points in the final grade. The second opportunity is governed by the same evaluation method. Each student who does not take the written theoretical-practical exam will be graded as a "no-show".
For the continuous assessment, students will carry out group and individual work to strengthen the competences CG2, CG3, CE6, CE7, CE8, CE9, CT1 and CT2. Additionally, group work is also good for competences CT3, CT4 and CT5. The final theoretical-practical exam will allow to work and evaluate, especially, the competences CG1, CG2, CG3, CG4, CE2, CE6, CE7 and CE8.
Working time required to pass the course relies heavily on prior knowledge and skill of the student. Normally, 1.5 hours of personal work (study of theoretical results and troubleshooting) for each hour of class, should be sufficient.
Having completed the core subjects of mathematics content of the degree and specifically: Linear and multilinear algebra, differentiation of functions of several real variables, linear and integer programming, probability and statistics.
To pass this subject, it is advisable to attend classes, and to solve and review the proposed exercises.
A virtual course will be offered on the USC platform, as a complement and support to the expository and interactive classes.
Language in which classes are taught: Spanish.
Balbina Virginia Casas Mendez
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813180
- balbina.casas.mendez [at] usc.es
- Category
- Professor: University Lecturer
| Tuesday | |||
|---|---|---|---|
| 17:00-18:00 | Grupo /CLE_01 | Spanish | Classroom 06 |
| Wednesday | |||
| 16:00-17:00 | Grupo /CLIS_01 | Spanish | Classroom 06 |
| 17:00-18:00 | Grupo /CLIS_02 | Spanish | Classroom 06 |
| Thursday | |||
| 16:00-17:00 | Grupo /CLIL_01 | Spanish | Classroom 06 |
| 17:00-18:00 | Grupo /CLIL_02 | Spanish | Classroom 06 |
| 05.26.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 07.11.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |