ECE 586TB
STATIC AND DYNAMIC GAME THEORY
This graduate-level course provides an
introduction to cooperative and noncooperative
game theory for both static and dynamic models, with deterministic as well as
stochastic descriptions. The coverage will encompass both theoretical and algorithmic
developments, with applications in engineering (control, communications, signal and
image processing, robotics, energy systems, transportation), biology, economics, and finance.
To follow the course, familiarity with dynamic systems (at the level of
ECE 515), some background in probability theory (at the level of ECE 313, and
preferably ECE 534), and some familiarity with the basics of linear and nonlinear programming
(at the level of ECE 490) are required.
FALL 2008 OFFERING
Instructor : Professor Tamer Başar
Office : 356 CSL (Phone: 3-3607)
Email : basar1@illinois.edu
Required Text 1:
Tamer Başar and Geert Jan Olsder, Dynamic Noncooperative Game Theory, 2nd edition,
Classics in Applied Mathematics, SIAM, Philadelphia, 1999.
Required Text 2:
G. Owen, Game Theory, 3rd edition, Academic Press, 1995
(for cooperative game theory)
Recommended Text
:
D. Fudenberg and J. Tirole,
Game Theory, MIT Press, 1991.
AND ...
readings from current and classical literature on game
theory
Meeting times : Tuesdays and Thursdays,
10:00 a.m. - 11:25 a.m. in 163 Everitt Lab
COURSE OUTLINE
-
Formulation of static and dynamic games. Cooperative vs noncooperative decision making;
introduction to various solution concepts. (1 1/2 hrs.)
-
Deterministic zero-sum and nonzero-sum static games: a) Matrix games, b)
Continuous-kernel games. Existence, uniqueness, and computation of noncooperative
equilibria. Fixed-point theorems (6 hrs.)
-
Cooperative games and bargaining: Characteristic functions; imputations; core;
Shapley value; nucleolus; applications. (6 hrs.)
-
Finite dynamic games: Notions of behavioral strategy, chance moves,
informational inferiority and nonuniqueness. Refinement of Nash
equilibrium: perfectness, properness, time consistency. (6 hrs.)
-
Evolutionary games and evolutionary stable strategies. (1 1/2 hrs.)
-
Formulation of and an introduction to infinite dynamic games.
Information structures; mixed and behavioral strategies on infinite-dimensional
spaces. (2 hrs.)
-
Deterministic infinite zero-sum dynamic games in discrete and continuous time.
Open-loop, feedback, and memory
saddle-point equilibria: existence, uniqueness, derivation, and computation.
(5 hrs.)
-
Applications to robust controller design in LQ systems. H-infinity bounds
and their computation. (2 hrs.)
-
Deterministic infinite nonzero-sum dynamic games
in discrete and continuous time.
Open-loop, feedback, and memory
Nash equilibria: existence, uniqueness, derivation, and refinement. (5 hrs.)
-
Deterministic infinite nonzero-sum dynamic games
with a hierarchical mode of play.
Open-loop and feedback Stackelberg
equilibria: existence, uniqueness, derivation, and computation.
Incentives: the principal-agent problem; applications in internet pricing and
electricity pricing. (6 hrs.)
-
An introduction to stochastic dynamic games: Markov games; noncooperative
equilibria under deterministic information patterns. (3 hrs.)
Other topics:
Term projects will cover other topics not included in the main lectures, such as:
- Discrete position (lattice) games with
delayed information
- Repeated games (e.g. repeated Prisoners' dilemma) and memory strategies
that support efficient equilibria under discounted or undiscounted
cost criteria
- Auction theory
- Sequential equilibria and strategic stability
- Singularly perturbed games; pursuit-evasion games and various applications
- Differential games with PDE descriptions
- Existence of value in deterministic and stochastic
zero-sum differential games; learning in dynamic and repeated games
- Applications of zero-sum dynamic game theory to communication
under jamming, robotic path planning with obstacles, watermarking, etc.
-
Applications of noncooperative nonzero-sum game theory and cooperative game theory
to resource management in communications.
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