| Title: Catastrophe Theory – Game Theory | Semester: Spring (2nd) |
| Tutors: G. Sarafopoulos, Professor – I. Psarianos, Assistant Professor |
Course Outline:
Catastrophe Theory
The lectures contain the following sections:
1. The concept of qualitative change. Examples
2. Introduction in elementary catastrophes
3. Classification of elementary catastrophes
4. Economic applications
Game Theory
- Static, non-cooperative and non-constant sum games of complete and perfect information
- The concept of strategy, weak and strong dominance
- Nash equilibrium in pure strategies
- Multiple Nash equilibria and indeterminacy
- Non-existence of Nash equilibria in pure strategies, repeated static games and Mixed Strategy Nash Equilibria
- Finite dynamic games of complete and perfect information
- Credibility, backwards induction and sub-game perfect Nash equilibrium
- Uncertainty and asymmetric information. Adverse Selection and Moral Hazard
Aim:
Catastrophe Theory
The aim of the course is to introduce the basic concepts of the approach, introduced by René Thom, in the description or interpretation of various phenomena and the presentation of its applications in economic theory.
The goal of R. Thom’s theory is to explain the appearance of discontinuities in continuous systems. The term “catastrophe” is therefore synonymous with the term discontinuity, but is used to give the idea of a dynamic that underlies phenomena. A catastrophe can be seen as violent, sudden changes of a system resulting from smooth changes in external conditions.
The fundamental result of the theory is the classification theorem, according to which if the parameters on which the potential function depends is at most 4, there are seven elementary catastrophes (7 types of discontinuity). There are only 7 types of potential functions that are «structurally stable» and give different qualitative results.
The principles of catastrophe theory are found in Singularity Theory of Whitney’s and in Poincaré, Andropov’s Bifurcation Theory. In particular, in a neighborhood of a critical non-degenerate point of a differentiable function the singularities are specific and of finite number, since in a suitable coordinate system the examined function is locally a quadratic form (Morse lemma). The theory of R. Thom adds, among other things, to this classic result the 7 elementary catastrophes for the degenerate critical points.
Game Theory
The course is an introduction to game theory and the applications it has to a broad range of topics that interest modern economic analysis and policy.
On completion of this module, students are expected to be able to:
¬ Understand the common complexity of a financial model
¬ Use the contemporary tools of the Financial Analysis
¬ Answer to new or non-answered questions
Suggested for further reading:
Catastrophe Theory
1. Arnold V.I., Catastrophe Theory, Springer-Verlag, 1984.
2. Ruelle D., Chaotic Evolution and Strange Attractors, Academia nazionale dei Lincei, 1989
3. Thom R., Structural Stability and Morphogenesis, W.A.Benjamin, 1975.
4. Whitney H., Mapping of the plane into a plane, Annals of Mathematics, vol 62,pp 374-470, 1955
5. Woodcock A., Davis M., Catastrophe Theory, Penguin Books Ltd,1980
6. Zeeman E.C., Catastrophe Theory (selected papers 1972-1977), Addison Wesley Reading, Massachusetts, 1977.
Game Theory
1. Baumol, W., Panzar J. and R. Willig, 1982. Contestable Markets and the Theory of Industry Structure. New York NY., Harcourt-Brace- Jovanovich.
2. Bierman S.H. and Fernandez L., 1998. Game Theory with Economic Applications. 2nd ed., New York NY., Addison-Wesley.
3. Camerer C., Loewenstein G. and Weber M., 1989. The Curse of Knowledge in Economic Settings: An Experimental Analysis, Journal of Political Economy, 97, 5, 1232-1254.
4. Gibbons R., 1992. Game Theory for Applied Economists. Princeton NJ., Princeton University Press.
5. McCain R., 2009. Game Theory and Public Policy. Northampton MA., Edward Elgar Publishing Inc.
6. McCain R., 2010. Game Theory. Revised ed. Hackensack NJ., World Scientific.
7. Nash J.F., 1950. The Bargaining Problem, Econometrica, 18, 155-162.
8. Nash, J.F., 1951. Non-Cooperative Games. Annals of Mathematics, 54, 286- 295.
9. Neumann, von J. and Morgenstern O., 1947. Theory of Games and Economic Behavior, Princeton NJ., Princeton University Press.
10. Radner, R., 1995. Games for Business and Economics. New York NY., John Wiley & Sons.
11. Schelling, T.C., 1980. The Strategy of Conflict. 2nd ed. Cambridge MA., Harvard University Press.
12. Μαγείρου, Ε.Φ., 2012. Παίγνια και Αποφάσεις, Μια εισαγωγική Προσέγγιση Νέα Αναθεωρημένη Έκδοση., Αθήνα, Εκδόσεις Κριτική.