Outline
Oligopoly
Game Theory
Dominant Strategy
Nash Equilibrium
Duopoly Models
-Cournot
-Bertrand
-Stackleberg
Monopolistic
Competition
Monopoly
Perfect
Competition
Oligopoly
Imperfect Competition:
-Market structures that fall between perfect competition and pure monopoly.
-Firms have competitors, but do not face so much competition that they are price takers.
Oligopoly
-Few sellers, each offering a similar or identical product to the others.
Monopolistic Competition
-Many firms selling products that are similar but not identical.
Because of few sellers…..
Collusion:
Cartel:
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Game Theory:
Strategic Decisions:
*Game theory studies interactive decision-making, where the outcome for each participant (player) depends on the
actions of all. If you are a player in such a game, when choosing your course of action (strategy), you must take into
account the choices of others. But thinking about their choices, you must recognize that they are thinking about
yours, and in turn trying to take into account your thinking about their thinking, and so on…..
Dominant Strategy:
Nash Equilibrium:
Coffee Production Example: pg 456
-cooperation: ↓output, ↑ prices
Lotterman Example: handout
-follow the leader
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Prisoner’s Dilemma:
2 Prisoners held separately for a crime they did commit
Without the testimony (confession) of at least 1 defendant, they each can only be convicted of a minor offense
Each is told that if they confess, they will go free & the other will get 20 years
If neither confesses, they each get 1 year
If both confess, they each get 5 years
No matter what X does, Y will do best by confessing
-Dominant strategy is to confess*
If X confesses, it follows that Y will get the following:
Silent =
Confess =
If X silent, it follows that Y will get the following:
Silent =
Confess =
No matter what Y does, X will do best by confessing
-Dominant strategy is to confess*
If Y confesses, it follows that X will get the following:
Silent =
Confess =
If Y silent, it follows that X will get the following:
Silent =
Confess =
Self interest……
The Prisoner’s Dilemma…….
The dominant strategy for each prisoner is to confess.
Nash Equilibrium: both confess
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Extending this example to firm behavior
Two firms facing market D:
Identical product
P = 20 – Q
MR = 20 – 2Q
MC = 0
20 – 2Q = 0
Cooperate = charge monopoly P and share monopoly Q
Defect = lower price and take entire market (lower P, higher Q)
Cooperate:
Qm = 10 (5 each)
Pm = $10
Profit = $100 ($50 each)
Defect:
P = $9
Q = 11 (5.5 each)
Profit = $99 ($99 and $0 respectively or $49.50 each)
No matter what 1 does, 2 will do best by defecting
-Dominant strategy is to defect*
If 1 defects, it follows that 2 will get the following:
Cooperate =
Defect =
If 1 cooperates, it follows that 2 will get the following:
Cooperate =
Defect =
No matter what 2 does, 1 will do best by defecting
-Dominant strategy is to defect*
If 2 defects, it follows that 1 will get the following:
Cooperate =
Defect =
If 2 cooperates, it follows that 1 will get the following:
Cooperate =
Defect =
Self interest…..
The Dilemma…….
The dominant strategy for each prisoner is to defect.
Nash Equilibrium: both defect
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It seems silly…..
But you can see how price competition could lead to driving price ↓ as firms continue to defect driving profits to 0.
This idea can be extended further to model advertising as well as research & development behavior
See pg. 459-460
Note:
In fact, a Nash equilibrium does not require both players to have a dominant strategy.
Other ideas……..
-Extended games, tit for tat, cold war, credible threat
-Sequential games and entry, Sears Tower, credible threat
-Firms that care about future profits may cooperate in repeated games rather than cheating to achieve a onetime gain.
-Cooperation among oligopolists is undesirable for society as a whole because it leads to ↓output, ↑ prices
Firms can compete in several ways……..
Quantity, Price, or even Quality
Pg. 467-475 and do examples and exercises
**Look for typos………
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Duopoly: 2 Firms selling an identical product
P = a – b(Q1 + Q2)
Market D:
V-int: P = a
(Q = 0)
P = a – bQ
H-int: Q = a/b
(P = 0)
Q = (Q1 + Q2)
slope = –b
Cournot Model: Competing in quantity (assume competitor’s Q is given)
-Given a particular Q2, firm 1 chooses Q1 to max profit
Firm 1’s D: P = (a – bQ2) – bQ1 **Residual D
Assume MC = 0
Shift vertical axis to right by Q2 (new axes, new origin)
V-int: P = a – bQ2
(Q1 = 0)
H-int: Q1 = a/b – Q2
(P = 0)
slope = –b
a/b
Now to find Q1* and P1*
MC = 0
Firm 1’s D: P = (a – bQ2) – bQ1
Use D to solve for P
MR1 = (a – bQ2) – 2bQ1
P = (a – bQ2) – bQ1
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MR = MC
Similarly for firm 2
Assume MC = 0
Shift vertical axis to right by Q1
V-int: P = a – bQ1
(Q2 = 0)
Now to find Q2* and P2*
(new axes, new origin)
H-int: Q2 = a/b – Q1
(P = 0)
slope = – b
MC = 0
Firm 2’s D: P = (a – bQ1) – bQ2
Use D to solve for P
Firm 2’s D: P = (a – bQ1) – bQ2
MR2 = (a – bQ1) – 2bQ2
P = (a – bQ1) – bQ2
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MR = MC
**Residual D
Equal output
 1  a 
Q1  Q2    
 3  b 
Logic
a/b
Q1 
a  bQ2
2b
Q1 = Q2
Math
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Cournot/Nash equilibrium?
Q such that each firm is doing the best it can, while taking the other firm’s choice of Q as given
Define Reaction Curves
Q1 *  R1 (Q2 ) 
a  bQ2
2b
V-int: Q1 = a/2b
(Q2 = 0)
Q2 *  R2 (Q1 ) 
V-int: Q1 = a/b
(Q2 = 0)
Q1, Q2 space
Q1 
a 1
 Q2
2b 2
slope = – ½
H-int: Q2 = a/b
(Q1 = 0)
a  bQ1
2b
Q1 
2bQ2  a  bQ1
slope = – 2
H-int: Q2 = a/2b
(Q1 = 0)
Solve for Equilibrium by setting R1 = R2
a
 2Q2
b
R1: Q1  a  1 Q2
2b 2
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R2: Q1  a  2Q2
b
We then find Price by plugging Q = (Q1 + Q2) into Market D
 2  a 
Q C  (Q1  Q2 )    
 3  b 
P = a – bQ
Profit = TR = P*Q
Comparing to cooperation (share monopoly outcome)
MR = a – 2bQ
a – 2bQ = 0
MC = 0
MR = MC
 1  a 
Q M    
 2  b 
 1  a 
P  a  b  
 2  b 
Profit = TR = P*Q
P = a - bQ
PM 
1
a
2
2
 1  1  a   1  a 
Pr ofit M   a       
 2  2  b   4  b 
Cournot Q > Monopoly Q
Cournot P < Monopoly P
Cournot Profit < Monopoly Profit
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Bertrand Story
Duopoly: 2 Firms selling an identical product
Bertrand Model: Competing in price
Each firm chooses best P given the other firm’s choice of P. Given a particular P2, firm 1 chooses P1 to max profit
*As we saw already in Prisoner’s Dilemma example
This will result in price war such that eventually price will be lowered all the way to MC resulting in zero profit
QB = a/b
efficient level of output
**This result mimics the result of Perfect Competition
You would follow same procedure here to mathematically get reaction functions R1(P2) = R2(P1)
a/b
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Model
Output
Price
Profit
Monopoly
 1  a 
Q M    
 2  b 
PM 
1
a
2
2
 1  a 
Pr ofit M    
 4  b 
Cournot
 2  a 
Q C    
 3  b 
PC 
1
a
3
 2  a
Pr ofit C   
 9  b
Stackelberg
 3  a 
Q S    
 4  b 
PS 
1
a
4
Bertrand
Perfect Competition
a
QB   
b
a
Q PC   
b



2
 3  a 
Pr ofit S    
 16  b 
2
PB = MC = 0
ProfitB = 0
PPC = MC = 0
ProfitPC = 0
**Extra Credit: Game Theory, Cournot, and Bertrand Examples
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