Game Theoretic Analysis of Oligopoly

1
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Game Theoretic Analysis of Oligopoly
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1
l
r
2
2
R
R
L
L
-10 -10
0 0
0 0
-10 -10
Rational Play is indicated by the black arrows
The Lane Selection Game
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1
l
r
2
2
Decision Nodes
R
R
L
L
-10 -10
0 0
0 0
-10 -10
Terminal Nodes
l, r and L, R are called choices
Top number in matrix is player 1s payoff
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A strategy is a contingency plan that specifies a
choice at each possible decision node
A best strategy of a player yields the maximum
payoff to him/her, for a specific strategy chosen
by the other player
A Nash Equilibrium is a strategy pair such that
each player plays his/her best strategy, given
the strategy of the other player
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A pure strategy is the choice of a strategy with
probability 1
A mixed strategy is a combination of two or more
strategies, each chosen with some positive
probability
A Dominant Strategy is such that it is the best
strategy of the player no matter what strategy is
chosen by the other
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• Player 2 s strategies
• (L if l, L if r),
• 2.R if l,and R if r

Player 1 s strategies are l and r
3. R if l), (L if r, 4.L if l,and R if r
Nash Equilibria l, L if l, R if r and r,
L if l R if r
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1
h
t

2
2
T
T
H
H
1 -1
1 -1
-1 1
-1 1
The Matching Pennies Game
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Player 2 has two pure strategies Hand T
Player 1 has two pure strategies h and t
The unique Nash Equilibrium (in mixed
strategies)is that each player mixes up each pure
strategy with 0.5 probability
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The Prisoners Dilemma
1
Y y stand for compete
N n stand for collude
n
y
2
2
N
N
Y
Y
5 -20
0 0
-5 -5
-20 5
A game of imperfect Information
The unique dominant strategy Nash Equilibrium is
(y,Y)
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1
n
y
2
2
N
N
Y
Y
5 -20
0 0
-5 -5
-20 5
The Prisoners Dilemma
A game of Perfect Information
The only play is (y, Y)
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1
T
B
M
2
2
R
C
R
L
L
C
0 10
10 3
-3 -4
-5 2
-2 11
3 4
2
L
R
C
12 -2
-3 -4
10 -1
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1- Entrant
3m 3m
-1m 2m
2- Incumbent
0 7m
Tough
Soft
2
Stay Out
Enter
Credible Threat Equilibrium
1
The two Nash Equilibria are
1 Stay Out 2 Tough if Enter
1 Enter 2 Soft if Enter
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Finitely Repeated Games
Prisoners Dilemma
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1
N n stand for collude
Y y stand for compete
n
y
2
2
Game 2
N
N
Y
Y
5 -20
0 0
-5 -5
-20 5
The Prisoners Dilemma
A game of Perfect Information
Player 1 plays y and player 2 plays Y if y and Y
if n at the only Nash Equilibrium
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1
N n stand for collude
Y y stand for compete
n
y
2
2
Game 200
N
N
Y
Y
5 -20
0 0
-5 -5
-20 5
The Prisoners Dilemma
A game of Perfect Information
Player 1 plays y and player 2 plays Y if y and Y
if n at the only Nash Equilibrium
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Finite Sequence of Entry Games
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1- Entrant
3m 3m
-1m 2m
2- Incumbent
Game with two sequential entries
0 7m
Tough
Soft
2
Stay Out
Enter
1
The two Nash Equilibria are
1 Stay Out 2 Tough if Enter
1 Enter 2 Soft if Enter
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1- Entrant
3m 3m
-1m 2m
2- Incumbent
Game with two hundred sequential entries
0 7m
Tough
Soft
2
Stay Out
Enter
1
The two Nash Equilibria are
1 Stay Out 2 Tough if Enter
1 Enter 2 Soft if Enter