The strategy, RL, could be
considered a threat since
it
ʼ
s not in Bob
ʼ
s best
interest to choose Right if
Alice chooses South.
-not a normative statement
Econ 221
Assignment #4 due on Tuesday, 22nd March
(in class)
Sub-game Perfect Nash Equilibrium
-In this scenario we break down the game tree into two sub-games, as shown below.
-Then we identify all the pure strategies that each player has.
S
Alice
= {
N, S
}
S
Bob
= {
LL
, LR, RL, RR
}
-And this is the game in Normal Form
Bob
LL
LR
RL
RR
N
(5, 2)
(5, 2)
(1, 0)
(1, 0)
Alice
S
(4, 4)
(6, 0)
(4, 4)
(6, 0)
-Therefore, there are two Nash equilibria: (N, LL) and (S, RL)
-If we go back to the tree, we can
look ahead and reason back
:
-this will tell us which of the two equilibria is the actual outcome of the game, highlighted by the red lines
--> this is called the Equilibrium Path
Prisoners
ʼ
Dilemma
Bob
Defect
Cooperate
Defect
(5, 2)
(5, 2)
Alice
Cooperate
(4, 4)
(6, 0)
March 15, 2011 - Lecture 17
Alice
North
Right
Right
South
(5, 2)
(1, 0)
(4, 4)
(6, 0)
Bob
Bob
X
Y
Equilibrium Path
Left