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prof.
Vladimir
I.Danilov
The
purpose of the course is to introduce basic concepts and results
of the modern game theory which are increasingly used in Economics.
The larger part of the course is devoted to noncooperative
game theory and its main concept of Nash equilibrium. Different
purified modifications of the concept are discussed also. The
second part of the course deals with cooperative game
theory and with concepts as core and Shapley’s vector.
Two
examinations are scheduled. The final grade will be based on
sections activity (40%) and examinations grades (30% each).
Course
Outline
Lecture
1. Games in the extensive and normal forms.
The
subject of the game theory. The normal form of a game.
Examples. Games in the extensive form. Strategies. Information
sets. Randomized choices.
Sections:
Relationships between the extensive and normal forms.
Lecture
2. Theory of the expected utility.
Basic
concepts of Bayesian theory of solutions. Objective
and subjective probability. Axioms of Bayesian theory.
The theory of expected utility. The uniqueness of the
utility. The generalization for non-additive probability
case.
Lecture
3. Dominance and best choices.
The
concept of a game’s solution. Best choices. Dominance.
Section:
Choice’s functions and an expected utility.
Lecture
4. Dominant strategies
Lecture
5. Cautious behavior
Section: Focal
points and dominance.
Lecture
6. Deletion of dominated strategies.
Deletion
of dominated strategies. Iterated deletion. The concept
of common knowledge. Resolvable games. Kuhn theorem.
Rationalizable strategies.
Lecture
7. Nash equilibrium.
Nash
equilibrium. Connection with former concepts. An importance
of Nash equilibrium. Competitive equilibrium as Nash
equilibrium. Applying for oligopoly.
Section:
Deletion of dominated strategies.
Lecture
8. Mixed expansions of games
Mixed
strategies. An existence of an equilibrium within mixed
strategies. Infinite games. Two-player zero-sum games.
Lecture
9. Sequential equilibrium
Behavioral
strategies in the extensive games. Sequential equilibrium.
Perfect subgame equilibrium. An example - vote game.
Section: Fining
Nash equilibrium.
Lecture
10 Perfect equilibrium
The
concept of perfect equilibrium. An existence of perfect
equilibrium. Subgame equilibrium. An existence.
Lecture
11 Repeated games
Repeated
Prisoner’s Dilemma. Repeated games general model. Repeated
games’ payoff criteria. Supergame. Supergame folk-theory.
The concept of information expansion of a game.
Mid-term
examination
Lecture
12. Bayesian games
Incomplete
information. The concept of a mechanism. Bayesian games.
Bayesian equilibrium. Example - auctions.
Lecture
13. Informed games.
Contracts
and correlated strategies. Correlated equilibrium. Communication
systems, noise. Bayesian informed games. Example - the
sender-receiver game.
Section
Purified Nash equilibrium.
Lecture
14. Tender problem
The
concept of tender problem. Status quo point. Nash solution,
its axiomatic structure. Another approaches - egalitarianism
and unitarianism.
Lecture15. Cooperative
game theory
Coalitions.
Games with transferable utility or collateral payoffs.
Game’s characteristic form. Divisions and solutions.
Section:
Tender problem.
Lecture
16. Core
Blocking.
The concept of a stable division. Core. Concave games
and its cores. Bondareva theorem of balanced games.
Section: Core
calculation.
Lecture
17. Shapley’s vector.
Axiomatic
definition of Shapley’s vector. Theorem of existence
and uniqueness of Shapley’s vector. Examples. Non-atom
games.
Lecture
18. Games without collateral payoffs.
Formalization
games without collateral payoffs. The concept of core
for these games. Scarf’s core theorem. Generalization
of Shapley’s vector. Game’s competitive equilibrium.
Section: Shapley’s
vector calculation.
Lecture
19. Cooperative choice.
Cooperative
choice problem. Aggregated preference. Arrow’s axioms,
dictator’s theorem. The concept of mechanism, non-manipulatively.
Lecture
20. Groves mechanism.
Quasi-linear
preference. Mechanisms with compensation. An example
of non-manipulated mechanism - second price auction.
Generalization - Clarke mechanism. Groves mechanisms
and their characteristics. Non-efficiency of Groves
mechanisms.
The
examination.
Recommended
readings:
R.B.
Myerson, Game Theory (Analysis of Conflict), Harvard University
Press, Cambridge, London, England, 1991
-
Mulen,
Game Theory, Moscow, Mir, 1985.
R.D.
Luce, H. Rife, Games and Solutions, Moscow, IL, 1961
-
Own,
Game Theory, Moscow, Mir, 1971
-
Fudenberg,
J. Tirole, Game Theory, Cambridge, Mass.: MIT Press, 1991
A.
Mas-Collel, M. Whinston, J. Green, Microeconomic Theory, N.-Y.,
Oxford Univ. Press, 1995
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