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NON-COOPERATIVE
GAMES IN ECONOMIC THEORY
3d Module, 2002/2003
Professor:
Alexander
Vasin
This
course aims to discuss applications of game theory to analysis
of actual economic problems. The course discusses the following
main themes.
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Models
of imperfect competition.
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Evolutional
Game Theory and description of economic behavior.
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Repeated
games and cooperative behavior.
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Models
of tax inspection organization.
The
proposed course consists of 14 lectures and includes two control
works. At the end of the course there is a final written examination.
Lectures are supplied by corresponding methodical material.
The
major textbooks for independent work are:
[1]
Danilov V.I., Koshevoy G.A. Game Theory. The course for the
first year students of the NES.
[2]
Myerson R.B. Game theory. Analysis of Conflict. Harvard University
Press, Cambridge, London, England, 1991
[3]
Moulin H. Game theory with economic examples. 1985
[4]
Mas-Colell A., Whinston M., Green J.R., Microeconomic theory.
1995
COURSE
OUTLINE
1.
Introduction.
Problems
of imperfect competition theory. Bertrand and Cournot models.
Basic concepts of non-cooperative game theory. Models of adaptation
and imitation behavior.
[1]
lectures 4,5,8
[2]
chs 1,3
Milgrom
P., Roberts J. (1990), Rationalizability, learning and equilibrium
in games with strategic complementaries. Econometrica, 58,
1255-1277
2.
Oligopoly Models.
Bertrand-Edgeworth
model. Iterative elimination of dominated strategies. Evaluation
of the market price deviation from the Walrasian price. Behavior
dynamics under price competition.
[1]
lecture 6
Microeconomics-1,
Oligopoly
Allen
B., Hellwig M.(1986), Bertrand-Edgeworth Oligopoly in Large
Markets, Review of Economic Studies, 53, 175-204
Borgers
T.(1992), Iterated Elimination of Dominated Strategies in
Bertrand-Edgeworth Model, Review of Economic Studies, 59,
163-176
Vasin
A.A.(1992), On Modelling of Collective Behavior in Social
and Ecological Systems, Moscow State University Computational
Mathematics and Cybernatics Bulletin, Vol.47,No.1,pp. 4-16
3.
Oligopoly Models (Continuation).
Model
with quantity and price leadership. Variable prices.
[3]
ch 5
Friedman
J. (1988), On the Strategic Importance of Prices Versus Quantities,
Rand Journal of Economics, N4, 607-622
Dudey
M. (1992), Dynamic Edgeworth-Bertrand competition. Quarterly
Journal of Economics, N4, 1461-1477
4.
Introduction to Evolutional Game Theory.
Games
of large groups (populations) of agents. Evolutional principle
of behavior formation. Static and dynamic approaches. Random
matching in pairs.
Vasin
A.A. (1996), On some problems of theory of collective behavior,
OPiPM, vol. 3, 346-365
Maynard
Smith J. (1982), Evolution and The Theory of Games, ch. 13
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Models
of collective behavior dynamics.
Replicator
dynamics. A notion of stable distribution over strategies.
Relation of attractors to Nash equilibria and dominant sets.
See lecture 2
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Models
of adaptation and imitation behavior.
Monotone
dynamics. Generalization of the theorem on relation between
attractors and game principles of optimality. Problem of stability.
Vasin
A. (1999) On stability of mixed equilibria, Nonlinear Analysis
38, 793-802
- Evolutional
mechanisms selection.
Theorem
on equilibrium mechanisms. Pecularities of evolution of behavior
in social populations. On manipulation of collective behavior.
Vasin
A. (1996)
8.
Conditions of perfect competition. Repeated bargaining in
pairs as a mechanism of equilibrium formation. Uncorrespondence
between Subgame perfect equilibrium (SPE) and Walrasian equilibrium
in Rubinstein-Wolinsky model.
Rubinstein
A., Wolinsky A.(1985), Equilibrium in a Market with Sequential
Bargaining, Econometrica, 53, 1133-1150
9.
The model by D. Gale. The theorem on the correspondence between
SPE and economical equilibrium. Bargaining in pairs at the markets
with two goods and the finite time.
Gale
D.(1986), Bargaining and Competition Part 1: Charecterization,
Econometrica, 54, 785-806
10.
Does repetition lead to cooperation? The Folk Theorem for
dominant solution. Construction of solution and pertubed payoff
functions. The case of outcome, which dominates Nash equilibrium
of original game.
A.A.Vasin."The
Folk theorem for dominance solutions", International Journal
of Game Theory (1999) 28:15-24.
11.
The model of partner selection. Conditions of correspondence
between the SPE and the utilitarian outcome. Evolution of cooperative
behavior. The case of groups with unequal number of members.
Vasin
(1992)
12.
Determination of optimal audit strategy for a direct tax.
The theorem on optimality of cut-off rule. Search for the optimal
threshold.
Sanchez,
I., Sobel, J., 1993, Hierarchical design and enforcement of income
tax policies’, Journal of Public Economics, 50, 345-69
A.
Vasin, E. Panova, 1999, “Tax Collection and Corruption”,
ERRC Working Paper Series
13.
Models with two levels of income and corruption. Agents’
behavior dependence on audit strategy. Comparable statics of tax
income with respect to tax and fine rates.
A. Vasin, E.Panova, 1999
14.
The problem of tax inspectors stimulation. Optimal system
of premiums for inspectors. The optimization of net tax revenue
in trasforming period.
P.
Chander, L. Wilde, 1992, “Corruption in tax administration”,
Journal of Public Economics, 49, 333-349
Mookherjee,
D. and Y. Png, (1989), Optimal auditing, insurance and redistribution,
Quarterly Journal of Economics, 104, 399-415
A.
Vasin, E. Panova, 1999
Prof.
Vasin A.A.,
Faculty of Computational Mathematics and Cybernetics,
Moscow State University,
119899, Moscow, Russia;
Tel./fax: (095)939-24-91, e-mail: vasin@cs.msu.su
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