Games and Decisions
Non Cooperative Games
2 commonly used representations:
o
o
Extensive form
Strategy form
Tree with a distinguished node is called the starting point (initial node)
o
Only requirement of a tree is no closed circle/circuit
An assignment o

Games and Decisions
Examples of Games:
Man (left)
Woman
SB
GL
SB
1,1
0,0
GL
0,0
1,1
Battle of the Sexes: Starbucks vs generic latte
o
This is a type of coordination game
Focal point: Place where people know other people congregate
L
R
T
9,5
0,0
B
0,0
2,2

Games and Decisions
Games with infinite number of strategies:
o
o
Games that inherently have an infinite number of strategies
Games with discreet strategies that we out probability distributions on
Market game - Nash-Cournot
o
- Nash-Stackleburg For both

Games and Decisions
First Order Commission for an Optimum
1
1
1 =
= ( ) 2 21 = 0
()2
2
-This the reaction function, otherwise known as the best response function
So through symmetry we know:
o
2 =
()1
2
o
o
R1Q2 represents firms reaction to q2
o
R2Q1 repr

Games and Decisions
Given a game = (Si Ui)N the joint strategy is a dominant strategy equilibrium of if for each
player Ui Ui( , ) for all in Si
in Si - A particular strategy for all possible players
= dominant strategy equilibrium (what should result f

Games and Decisions
Cost Functions
C1(Q1) is the cost for firm 1
o
This cost depends on the number of units the firm produces
C2(Q2) is the cost for firm 2
So through these equations, we are seeing that each firms costs only depend on the number of
units

Games and Decisions
Cournot Equilbrium occurs when each firm maximizes its output given the output of the
other firm
Cournot Equilibirum requires best response functions
Example of Nash Cournot:
Demand for product P = 12 (q1 + q2) (perfect substitution be

Games & Decisions
In a game between firm 1 and firm 2, what if firm 1 is a monopolist?
o
q2 = 0
o
1(q1 , q2) = [(12 (11/2) 0)q1m] q1m (11/2 = q1m, 0 = q2,)
o
o
)=
o
)
o
)
o
o
o
Therefore, if firm 1 was monopolist, its profits would be greater than the tot

Games & Decisions
If N is large, approximate to infinity
o
o
o
o
o
o
MC = Marginal Cost
Mixed Strategy Nash Equilibrium
Heads (left)
Tails
H
1,-1
-1,1
H
T
(1-q) = probability of picking heads or tails
(1-p) = probability of picking heads or tails
Player 1

Games & Decisions
Imperfect Info game: Dont know which node you are on; It can be a sequential game but it
doesnt matter because you dont know where you will be so you can make your choice
whenever
o
So the fact that a game is sequential is meaningless, w