Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare si simulare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MME1010	Modeling of Economical Processes	

Semester	Hours: C+S+L	Category	Status	
4	2+2+0	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
PETRUSEL Adrian Olimpiu	Ph.D.	Prof.	Differential Equations	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The goal of this course is to provide students with some models and problems of mathematical economics. After completing the course, the students will have basic concepts and tools of mathematical economics and they should be able to analyse and diagnose the behavior of some actual economical process.	

IV. Course contents
Course 1. Arrow-Debreu model. 
Seminar 1. The functionals D, Delta, Rho and H (exercises and examples)
Course 2. The concept of generalized game and abstract economy.
Seminar 2. Hausdorff-Pompeiu metric (exercises and properties) 
Course 3. Continuity concepts for multivalued operators. 
Seminar 3. Examples and exercises in connection to the continuity of multivalued operators. 
Course 4. Selection results for multivalued operators. The continuous case. 
Seminar 4. Lipschitz-type multivalued operators. Basic properties. 
Course 5. Topological fixed point theorems for multivalued operators. 
Seminar 5. Examples and counterexamples for topological fixed point theorems. References: [4]-pages 533-540, [6]-pages 99-104.
Course 6. Properties of the fixed point set. 
Seminar 6. Middle Term Written Test
Course 7. KKM lemma.
Seminar 7. Examples and exercises, particular cases of KKM lemma. 
Course 8. Applications of KKM lemma to variational inequalities and game theory.
Seminar 8. Caristi&#8217;s theorem. Applications and extensions. 
Course 9. Stability results for the KKM set.
Seminar 9. (Report): Maximal elements. 
Course 10. Coincidence theorems and applications to Nash equilibrium points. 
Seminar 10 Coincidence theorems for singlevalued and multivalued operators. 
Course 11. Strict fixed point theorems.
Seminar 11 Strict fixed point theorems. 
Course 12. Existence results for equilibrium points. 
Seminar 12. Existence for Walras-type equilibrium. 
Course 13. The excess-demand multifunction.  
Seminar 13. Equilibrium price for the excess-demand multifunction. 
Course 14. New research directions in mathematical economics. 
Seminar 14. Models of written tests. Presentation of the grades obtained during the semester evaluation.

V. Bibliography
1)  G. Mot, A. Petrusel, G. Petrusel: Topics in Nonlinear Analysis and Applications to Mathematical Economics, House of the Book of Science, Cluj-Napoca, 2007. 
2)  J.P. Aubin: Optima and Eqilibria, Springer, Berlin, 1993. 
3)  G.X.Z. Yuan: KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker, New York, 1999. 
4)  K. Border: Fixed Point Theorems with Applications to Economic and Game Theory, Cambridge University Press, London, 1985. 
5)  J. Dugundji, A. Granas.: Fixed Point Theory,.  Springer-Verlag, Berlin, 2003.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
The final grade is the weighted mean of the following three grades. 
The final grade = 50% Final Written Test + 25% Middle Term Written Test + 25% Report.  Successful passing of the exam is conditioned by the final grade that has to be at least 5. 
All university official rules with respect to students&#8217; attendance of academic activities, as well as to cheating and plagiarism, are valid and enforced. 

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Prof. PETRUSEL Adrian Olimpiu, Ph.D.