Economics 405/505
Rui Zhao
1
Introduction to Game Theory
University at Albany, SUNY
Strategic Games: Theory
1.1
General Idea
A strategic game has three essential components.
1. There is a set of players, 1, ., i, ., I.
2. Each player i has a set of strate
Economics 405/505
Prof. Rui Zhao
Introduction to Game Theory
University at Albany
Some Applications of Nash Equilibrium and Best Response Functions
Cournot Oligopoly
The outcome of the competition among oligopoly rms depends on the
market demand for rms o
Economics 405/505
Prof. Rui Zhao
Introduction to Game Theory
Mixed Strategies
Motivating Example: The following Matching Pennies game does not
have a pure strategy Nash equilibrium.
payos
Heads
Tails
1
Heads
1, -1
-1, 1
Tails
-1, 1
1, -1
Probability
1.1
P
Economics 405/505
Rui Zhao
Introduction to Game Theory
Applications of Extensive-form Games
1
1.1
Stackelberg Model of Duopoly
General Model
Two rms produce identical products. Firm 1 chooses its output q1 rst. Firm 2, after
observing q1 , chooses its out
Economics 405/505
Prof. Rui Zhao
Introduction to Game Theory
Repeated Games
Stage game:
L
M
R
L (1, 1) (5, 0) (1, 0)
M (0, 5) (4, 4) (0, 0)
R (0, 1) (0, 0) (3, 3)
There are two pure-strategy Nash: (L, L), (R, R).
In the twice-repeated game, there is an SP
Economics 405/505
Prof. Rui Zhao
Introduction to Game Theory
Static Games with Incomplete Information
1. Structure of Games with Incomplete Information
In a game with incomplete information, before the game starts some (or
all) players already have some i