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
To 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 games strategically.
Examples: Cournot oligopoly and Bertrand , auctions, etc .
Nash equilibrium in games strategically. 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 games.
Nash equilibrium in extensive games . Kuhn 's Theorem.
Introduction to the refinements of Nash equilibrium in extensive 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.
BIBLIOGRAFÍA BÁSICA
B. Casas Méndez, G. Fiestras Janeiro, I. García Jurado y J. González Díaz (2012). "Introducción a la Teoría de Juegos''. USC Editora. Consulta online: https://prelo.usc.es/Record/Xebook1-207
H. Peters (2015) "Game Theory". Ed. Springer.
Consulta online: https://link.springer.com/book/10.1007%2F978-3-662-46950-7
BIBLIOGRAFÍA COMPLEMENTARIA
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. Consulta online:
https://link.springer.com/book/10.1007%2F978-3-642-37434-0
T. Driessen (1988). "Cooperative Games, Solutions and Applications''. Kluwer Academic Publishers.
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. Consulta 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.
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.
J. von Neumann and O. Morgenstern (1947). "Theory of Games and Economic Behavior''. Princeton University Press.
GENERAL AND SPECIFIC
Knowledge of the most important models, concepts and results of game theory.
Ability to stimulate 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 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.
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.
SCENARIO 1 (adapted normality):
The expository and interactive teaching will be face-to-face and 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 email.
SCENARIO 2 (distancing):
Partially non-face-to-face teaching, according to the distribution organized by the Faculty of Mathematics. The tutorials will be attended by email or through MS Teams.
SCENARIO 3 (closure of the facilities):
Totally non-classroom teaching through the virtual campus and MS TEAMS. Tutoring by email or MS Teams.
SCENARIO 1 (adapted normality):
The student can take advantage of one of the following modalities:
Modality 1.1. Through continuous evaluation according to the following score:
class attendance (0.5 pts.), delivery through the virtual campus (CV) and exhibition of group work in tutorials in very small groups (1.5 pts.), control 1 in the classroom (2 pts.), delivery of individual work through the CV (2 points), control 2 in the classroom (4 points).
Modality 1.2. Through continuous assessment plus final written exam according to the following score:
class attendance (0.125 pts.), delivery through the CV and presentation of group work in tutorials in very small groups (0.375 pts.), control 1 in the classroom (0.5 pts.), delivery of individual work through the CV (0.5 points), control 2 in the classroom (1 point), final written exam (7.5 points, of which 2.5 correspond to theory questions and 5 to problems).
Mode 1.3. Final written exam (10 pts.)
The second opportunity will have Modalities 1.2 and 1.3 previously described.
SCENARIO 2 (distancing):
The same procedure as that described for SCENARIO 1 with the only difference that some of the controls and the final exam could be non-face-to-face as circumstances warrant. Assistance is understood to be either physical or online.
SCENARIO 3 (closure of the facilities):
The same procedure as that described for SCENARIO 1 with the only difference that the presentation of the group work, the controls and the final exam would become non-presential. In this case the assistance would be online (through MS TEAMS).
Students who do not pass the subject by continuous assessment and do not take the theoretical-practical written exam will be graded "not presented".
For continuous assessment, students will carry out group and individual work to strengthen CG2, CG3, CE6, CE7, CE8, CE9, CT1 and CT2. Additionally, group work is also good for skills CT3, CT4 and CT5. The theoretical-practical final exam will allow working and evaluating, 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, two 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.
Contingency plan against COVID 19:
If the health situation requires it and according to the indications established by the academic authorities, the methodology and evaluation will be adapted to the SCENARIO (2 or 3, as appropriate) as explained above.
In cases of fraudulent performance of exercises or tests, the provisions of the regulations of the University of Santiago de Compostela will apply.
This guide and the criteria and methodologies described therein are subject to modifications derived from regulations and directives of the University of Santiago de Compostela.
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
Laura Davila Pena
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813391
- laura.davila [at] rai.usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 15:00-16:00 | Grupo /CLIS_01 | Spanish | Ramón María Aller Ulloa Main Hall |
| Tuesday | |||
| 15:00-16:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| Wednesday | |||
| 15:00-16:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| Thursday | |||
| 15:00-16:00 | Grupo /CLIL_02 | Galician, Spanish | Classroom 03 |
| 16:00-17:00 | Grupo /CLIL_01 | Galician, Spanish | Classroom 03 |
| 06.03.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02 |
| 06.03.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 03 |
| 06.03.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 06.03.2021 16:00-20:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 07.08.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02 |