Deep Thought
To me, boxing is like a ballet, except
there’s no music, no choreography,
and the dancers hit each other. ~
Jack Handey.
(Translation: Today’s lesson teaches how to manage a company
recognizing competitors are selling substitute products.)
BA 210 Lesson II.5 Simultaneous Quantity Competition
1
Lesson overview
Lesson II.5 Simultaneous Quantity Competition
Example 1: Cournot Duopoly
Example 2: Nash Equilibrium
Example 3: First Mover Advantage
Example 4: Selling Technology
Example 5: Colluding
Example 6: Merging
Summary
Review Questions
BA 210 Lesson II.5 Simultaneous Quantity Competition
2
Example 1: Cournot Duopoly
Example 1: Cournot Duopoly
BA 210 Lesson II.5 Simultaneous Quantity Competition
3
Example 1: Cournot Duopoly
Comment: Cournot Duopoly Games have three parts.
• Players are managers of two firms serving many consumers.
• Strategies are outputs of homogeneous products (perfect
substitutes), so they sell at the same price P.
• Firm 1 chooses output Q1 > 0.
• Firm 2 chooses output Q2 > 0.
• Each chooses either chooses output simultaneously, or
chooses sequentially but the one that chooses second
does not know the choice of the one that chooses first.
• Payoffs are profits. When unit production costs of production
are constants c1 and c2, then profits are
P1 = (P- c1)Q1 and P2 = (P- c2)Q2
BA 210 Lesson II.5 Simultaneous Quantity Competition
4
Example 1: Cournot Duopoly
Payoffs for the two players often listed in a table. The strategies
are listed as rows for Player 1, and columns for Player 2. The
combination of strategies by both players determines a cell in the
payoff table, and that cell specifies the payoffs to the players,
with Player 1 listed first. For example, if Player 1 chooses Q1=3
and Player 2 chooses Q1=1, then in the payoff table below 12,5
specifies payoff 12 to Player 1 and 5 to Player 2.
Player 2
Player 1
1
3
4
1
6,7
12,5
12,4
3
4,15
6,9
4,6
BA 210 Lesson II.5 Simultaneous Quantity Competition
4
3,16
3,8
0,4
5
Example 1: Cournot Duopoly
Question: Intel and AMD simultaneously decide on the size of
manufacturing plants for the next generation of microprocessors
for consumer desktop computers. Suppose the firms’ goods are
perfect substitutes, and market demand defines a linear inverse
demand curve P = 20 – (QI + QA), where output quantities QI and
QA are the thousands of processors produced weekly by Intel and
AMD. Suppose unit costs of production are cI = 1.1 and cA = 1.1
for both Intel and AMD. Suppose Intel and AMD consider any
quantities QI = 3, 5, 6, 7, 9 and QA = 3, 5, 6, 7, 9.
What quantity should Intel produce?
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
Example 1: Cournot Duopoly
Answer: Intel’s quantities QI = 3, 5, 6, 7, 9 are on the rows, and
AMD’s quantities QA = 3, 5, 6, 7, 9 are on the columns in the
following normal form. For example, QI = 3 and QA = 5
generates price P = 20-8 = 12, and profits PI = (12-1.1)3 = 32.7
and PA = (12-1.1)5 = 54.5. (On an exam, I would provide most
entries.)
20
Intel
1.1
1.1
3
5
6
7
9
AMD
3
38.7,38.7
54.5,32.7
59.4,29.7
62.3,26.7
62.1,20.7
5
32.7,54.5
44.5,44.5
47.4,39.5
48.3,34.5
44.1,24.5
6
29.7,59.4
39.5,47.4
41.4,41.4
41.3,35.4
35.1,23.4
7
26.7,62.3
34.5,48.3
35.4,41.3
34.3,34.3
26.1,20.3
BA 210 Lesson II.5 Simultaneous Quantity Competition
9
20.7,62.1
24.5,44.1
23.4,35.1
20.3,26.1
8.1,8.1
7
Example 1: Cournot Duopoly
Strategy 3 is dominated for each player (by Strategy 5) and
Strategy 9 is dominated for each player (by Strategy 7). Hence,
eliminate those strategies, leaving the normal form:
20
Intel
1.1
1.1
3
5
6
7
9
AMD
3
38.7,38.7
54.5,32.7
59.4,29.7
62.3,26.7
62.1,20.7
5
32.7,54.5
44.5,44.5
47.4,39.5
48.3,34.5
44.1,24.5
6
29.7,59.4
39.5,47.4
41.4,41.4
41.3,35.4
35.1,23.4
7
26.7,62.3
34.5,48.3
35.4,41.3
34.3,34.3
26.1,20.3
BA 210 Lesson II.5 Simultaneous Quantity Competition
9
20.7,62.1
24.5,44.1
23.4,35.1
20.3,26.1
8.1,8.1
8
Example 1: Cournot Duopoly
Strategy 5 is now dominated for each player (by Strategy 6).
Hence, eliminate that strategy, leaving the normal form:
20
Intel
1.1
1.1
3
5
6
7
9
AMD
3
38.7,38.7
54.5,32.7
59.4,29.7
62.3,26.7
62.1,20.7
5
32.7,54.5
44.5,44.5
47.4,39.5
48.3,34.5
44.1,24.5
6
29.7,59.4
39.5,47.4
41.4,41.4
41.3,35.4
35.1,23.4
7
26.7,62.3
34.5,48.3
35.4,41.3
34.3,34.3
26.1,20.3
BA 210 Lesson II.5 Simultaneous Quantity Competition
9
20.7,62.1
24.5,44.1
23.4,35.1
20.3,26.1
8.1,8.1
9
Example 1: Cournot Duopoly
Strategy 7 is now dominated for each player (by Strategy 6).
Hence, eliminate that strategy, leaving only strategies QI = 6 and
QA = 6, and profits PI = 41.4 and PA = 41.4. As in any game,
under game theory assumptions (including rationality), it is
always best to play your strategy that is part of a dominance
solution.
20
Intel
1.1
1.1
3
5
6
7
9
AMD
3
38.7,38.7
54.5,32.7
59.4,29.7
62.3,26.7
62.1,20.7
5
32.7,54.5
44.5,44.5
47.4,39.5
48.3,34.5
44.1,24.5
6
29.7,59.4
39.5,47.4
41.4,41.4
41.3,35.4
35.1,23.4
7
26.7,62.3
34.5,48.3
35.4,41.3
34.3,34.3
26.1,20.3
BA 210 Lesson II.5 Simultaneous Quantity Competition
9
20.7,62.1
24.5,44.1
23.4,35.1
20.3,26.1
8.1,8.1
10
Example 1: Cournot Duopoly
Comment: The dominance solution QI = 6 and QA = 6, with
profits PI = 41.4 and PA = 41.4, is the only Nash Equilibrium. A
Nash Equilibrium means QI = 6 is Intel’s best response to QA = 6,
and QA = 6 is AMD’s best response to QI = 6.
20
Intel
1.1
1.1
3
5
6
7
9
AMD
3
38.7,38.7
54.5,32.7
59.4,29.7
62.3,26.7
62.1,20.7
5
32.7,54.5
44.5,44.5
47.4,39.5
48.3,34.5
44.1,24.5
6
29.7,59.4
39.5,47.4
41.4,41.4
41.3,35.4
35.1,23.4
7
26.7,62.3
34.5,48.3
35.4,41.3
34.3,34.3
26.1,20.3
BA 210 Lesson II.5 Simultaneous Quantity Competition
9
20.7,62.1
24.5,44.1
23.4,35.1
20.3,26.1
8.1,8.1
11
Example 2: Nash Equilibrium
Example 2: Nash Equilibrium
BA 210 Lesson II.5 Simultaneous Quantity Competition
12
Example 2: Nash Equilibrium
Comment: Although Cournot Duopoly Games have dominance
solutions even when quantities can be continuous variables
(including fractions), it is hard go through the entire sequence of
reasoning like in Example 1. It turns out, however, that the
unique dominance solution of a Cournot Duopoly Game is also
the unique Nash Equilibrium of the Game. And finding a Nash
Equilibrium is relatively simple.
A Nash Equilibrium of any game with two or more players means
each player is assumed to know the chosen strategies of the other
players, and each player chooses a best response to those chosen
strategies --- that is, no player has anything to gain by changing
only his or her own strategy unilaterally.
BA 210 Lesson II.5 Simultaneous Quantity Competition
13
Example 2: Nash Equilibrium
Question: You are a manager of Pepsi and you compete directly
with Coke selling soft drinks. Consumers find the two products
to be indistinguishable. The inverse market demand for soft
drinks is P = 11-Q (in dollars). Your unit costs of production are
$3, and the unit costs of Coke are $2. Compute profits when you
produce 1 units and Coke produces 6 units. Suppose profits from
other combinations of production are in the table below:
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
?,?
-3,0
-24,-18
14
Example 2: Nash Equilibrium
Question (continued): Suppose you choose your output of soft
drinks to be either 1, 3, or 4 at the same time that Coke chooses
its own own output of either 1, 3, or 4.
How many soft drinks should you produce?
BA 210 Lesson II.5 Simultaneous Quantity Competition
15
Example 2: Nash Equilibrium
Answer: You are the row player (Player 1) in a Cournot Duopoly
Game with inverse demand P = 11 - (Q1+Q2) and unit costs c1 =
3 and c2 = 2. If you produce Q1=1 units and DC produces Q2=6
units, then total output is Q1+Q2=7, so price is P = 11 (Q1+Q2)=4, and profits are
P1 = (P- c1)Q1 = (4-3)1 = 1 and P2 = (P- c2)Q2 = (4-2)6 = 12,
which we write 1,12 to complete the profit table.
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
1,12
-3,0
-24,-18
16
Example 2: Nash Equilibrium
Find the Nash Equilibrium to the Cournot Duopoly Game (which
turns out to be the dominance solution).
• if you believe Coke chooses Q2=1, then you respond with Q1=3.
But, if Coke believes you choose Q1=3, then they would not
actually choose Q2=1. So no Nash Equilibrium here.
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
1,12
-3,0
-24,-18
17
Example 2: Nash Equilibrium
• if you believe Coke chooses Q2=3, then you respond with Q1=3.
And if Coke believes you choose Q1=3, then they would indeed
choose Q2=3. So Q1=3 and Q2=3 is a Nash Equilibrium.
Is there any other Nash Equilibrium?
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
1,12
-3,0
-24,-18
18
Example 2: Nash Equilibrium
• if you believe Coke chooses Q2=6, then you respond with Q1=1.
But, if Coke believes you choose Q1=1, then they would not
actually choose Q2=1. So no Nash Equilibrium here.
Conclusion: Pepsi should produce 3 soft drinks and expect Coke
to produce 3 soft drinks.
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
1,12
-3,0
-24,-18
19
Example 2: Nash Equilibrium
Comment: The Nash equilibrium of Pepsi producing 3 soft drinks
and Coke producing 3 soft drinks is the unique dominance
solution. First, producing 6 is dominated for each player by
producing 3. After producing 6 is eliminated, producing 1 soft
drink is dominated for each player by producing 3.
Coke
Pepsi
1
3
6
1
6,7
12,5
6,2
3
4,15
6,9
-6,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
6
1,12
-3,0
-24,-18
20
Example 3: First Mover Advantage
Example 3: First Mover Advantage
BA 210 Lesson II.5 Simultaneous Quantity Competition
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Example 3: First Mover Advantage
Comment: If the unit production costs are the same for two firms
in a duopoly, then profits for Firm 1 are higher if that firm is the
leader in a Stackelberg duopoly rather than a firm in a Cournot
duopoly. And profits for Firm 1 are higher if that firm is in a
Cournot duopoly rather than the follower in a Stackelberg
duopoly.
In particular, a firm can find it profitable to become the first
mover by rushing to set up an assembly line, even if it means
increasing unit costs of production.
BA 210 Lesson II.5 Simultaneous Quantity Competition
22
Example 3: First Mover Advantage
Question: You are a manager of PetroChina and you compete
directly with Sinopec in Chinese oil production and distribution.
Consumers find the two products to be indistinguishable. The
inverse market demand for Chinese oil is P = 11-Q (in yuan) and
both firms produce either 1, 3, or 6 units at a unit cost of 2 yuan.
You have a decision to make about competing with Sinopec in
Siberia, where the inverse market demand for Chinese oil is P =
11-Q (in rubles). You must choose the option that is best for
PetroChina.
BA 210 Lesson II.5 Simultaneous Quantity Competition
23
Example 3: First Mover Advantage
Option A. Sinopec sets up its refineries and distribution networks
now, and you set up later. And both produce at a unit cost of 2
rubles.
Option B. You hurry set up your refineries and distribution
networks at the same time as Sinopec. Your hurry means your
unit costs are 3 rubles, while Sinopec’s costs remain 2 rubles.
Which Option is better for PetroChina?
BA 210 Lesson II.5 Simultaneous Quantity Competition
24
Example 3: First Mover Advantage
Answer: In Option A, you are the follower in a Stackelberg
Duopoly with inverse demand P = 11 - (Q1+Q2) and unit costs c1
= 2 and c2 = 2. In Option B, you are Firm 2 in a Cournot Duopoly
with inverse demand P = 11 - (Q1+Q2) and unit costs c1 = 3 and
c2 = 2.
BA 210 Lesson II.5 Simultaneous Quantity Competition
25
Example 3: First Mover Advantage
Option A. Sinopec sets up its
factories and distribution
networks now, and you set up
later. And both produce at a
unit cost of 2, resulting in the
first profit table:
Option B. You hurry set up
your refineries and distribution
networks at the same time as
Sinopec. Your hurry means
your unit costs are 3, while
Sinopec’s unit costs remain 2
resulting in the second profit
table:
Petro
Sinopec
1
3
6
1
7,7
15,5
12,2
3
5,15
9,9
0,0
6
2,12
0,0
-18,-18
Petro
Sinopec
1
3
6
1
7,6
15,4
12,1
BA 210 Lesson II.5 Simultaneous Quantity Competition
3
5,12
9,6
0,-3
6
2,6
0,-6
-18,-24
26
Example 3: First Mover Advantage
Answer: In Option A, you are
the follower in a Stackelberg
Duopoly. Sinopec anticipates
your reactions on the right, and
so chooses to produce 6, you
react with 1 and so you earn 2.
In Option B, you are in a
Cournot Duopoly. The only
Nash equilibrium and
dominance solution (eliminate
6, then eliminate 1) is Sinopec
chooses 3 and you choose 3,
and so you earn 6.
Petro
Sinopec
1
3
6
1
7,7
15,5
12,2
3
5,15
9,9
0,0
6
2,12
0,0
-18,-18
Petro
Sinopec
1
3
6
1
7,6
15,4
12,1
BA 210 Lesson II.5 Simultaneous Quantity Competition
3
5,12
9,6
0,-3
6
2,6
0,-6
-18,-24
27
Example 3: First Mover Advantage
Option B is thus best for PetroChina since PetroChina profits (as
a Stackelberg follower) are 2 in Option A, while PetroChina
profits (as a Cournot Duopolist) are 6 in Option B.
BA 210 Lesson II.5 Simultaneous Quantity Competition
28
Example 3: First Mover Advantage
Comment: In this particular case, PetroChina increased
production cost hurt profits less than profits increase because of
eliminating the second mover disadvantage. In other problems,
increased production cost hurt profits more than profits increase
because of eliminating the second mover disadvantage.
BA 210 Lesson II.5 Simultaneous Quantity Competition
29
Example 4: Selling Technology
Example 4: Selling Technology
BA 210 Lesson II.5 Simultaneous Quantity Competition
30
Example 4: Selling Technology
Question: You are a manager of Nvidia and your only significant
competitor in the mainstream graphics card market is the ATI
subsidiary of Advanced Micro Devices. You and ATI both
expect to produce the next generation of graphics card in October
of next year. Your graphics cards and ATI’s graphics cards are
indistinguishable to consumers. The inverse market demand for
graphics cards is P = 11-Q (in dollars) and both firms used to
produce at a unit cost of $2. However, you just found a better
way to produce graphics cards, which reduces your unit cost to
$1. Should you keep that procedure to yourself? Or is it better to
sell that secret to ATI so that both you and ATI can produce at
unit cost equal to $1?
To answer the questions, suppose both Nvidia and ATI separately
choose to produce either 1, or 2, or 3 units of graphics cards.
BA 210 Lesson II.5 Simultaneous Quantity Competition
31
Example 4: Selling Technology
Answer: If you do not sell your technology, you are Firm 1 in a
Cournot Duopoly with inverse demand P = 11 - (Q1+Q2) and unit
costs are c1 = 1 and c2 = 2; if you do sell, unit costs are c1 = 1 and
c2 = 1.
Find the Nash Equilibrium to each Cournot Duopoly Game
(which turns out to be the dominance solution).
BA 210 Lesson II.5 Simultaneous Quantity Competition
32
Example 4: Selling Technology
If you do not sell your technology, compute the payoff table and
Nash equilibrium for unit costs c1 = 1 and c2 = 2: The only Nash
equilibrium and dominance solution (eliminate 1 and 2) is Nvidia
chooses 3 and ATI chooses 3, and so Nvidia earns 12 and ATI
earns 9.
ATI
Nvidia
1
2
3
1
8,7
14,6
18,5
2
7,12
12,10
15,8
BA 210 Lesson II.5 Simultaneous Quantity Competition
3
6,15
10,12
12,9
33
Example 4: Selling Technology
If you do sell your technology, compute the payoff table and
Nash equilibrium for unit costs c1 = 1 and c2 = 1: The only Nash
equilibrium and dominance solution (eliminate 1 and 2) is Nvidia
chooses 3 and ATI chooses 3, and so Nvidia earns 12 and ATI
earns 12.
ATI
Nvidia
1
2
3
1
8,8
14,7
18,6
2
7,14
12,12
15,10
BA 210 Lesson II.5 Simultaneous Quantity Competition
3
6,18
10,15
12,12
34
Example 4: Selling Technology
Selling technology and reducing c2 = 2 to c2 = 1 has two potential
effects:
• Firm 1’s profit could change. But in this case, it remains at P1
= 12
• Firm 2’s profit increases from P2 = 9 to P2 = 12
Nvidia should sell the technology because doing so increases
total profit from production from 21 to 24, so there are 3 gains
from trade to be divided between the two firms according to the
rules of the resulting bargaining game. For example, if Nvidia
can make a credible take-it-or-leave-it offer of 3 minus a pittance
as the price of the technology to ATI, then Nvidia captures most
of those gains.
BA 210 Lesson II.5 Simultaneous Quantity Competition
35
Example 5: Colluding
Example 5: Colluding
BA 210 Lesson II.5 Simultaneous Quantity Competition
36
Example 5: Colluding
Question: The Mexican Multimedia market consists of two firms:
TV Azteca and Televisa. As a manager of TV Azteca, you
choose the number of broadcast hours of television programming
of your hit shows (Lo que callamos las mujeres, Ventaneando,
Hechos, Venga la Alegria, …) to air 1 hour before your
competitor, but Televisa does not have any way to know your
broadcast hours before choosing their own broadcast hours.
Advertisers consider all broadcast hours to be identical. The
demand for broadcast hours is Q = 13 - P; both firms’ unit costs
are 1; both firms separately produce either 1, 3, or 4 units.
Would it be mutually profitable for the companies to collude by
setting TV Azteca’s and Televisa’s outputs to 3 and 3. Can TV
Azteca trust Televisa to collude? Can Televisa trust TV Azteca?
BA 210 Lesson II.5 Simultaneous Quantity Competition
37
Example 5: Colluding
Answer: You are Firm 1 in a Cournot Duopoly with demand Q =
13 - P, inverse demand P = 13- (Q1+Q2), and unit costs c1 = 1
and c2 = 1.
Find the Nash Equilibrium to the Cournot Duopoly Game (which
turns out to be the dominance solution), and compare the Nash
Equilibrium to the collusive proposal of quantities 3 and 3.
BA 210 Lesson II.5 Simultaneous Quantity Competition
38
Example 5: Colluding
Compute the payoff table and Nash equilibrium for inverse
demand P = 13- (Q1+Q2), and unit costs c1 = 1 and c2 = 1: The
only Nash equilibrium and dominance solution (eliminate 1 and
3) is TV Azteca chooses 4 and Televisa chooses 4, and so TV
Azteca earns 16 and Televisa earns 16.
Televisa
Azteca
1
3
4
1
10,10
24,8
28,7
3
8,24
18,18
20,15
BA 210 Lesson II.5 Simultaneous Quantity Competition
4
7,28
15,20
16,16
39
Example 5: Colluding
Setting TV Azteca’s and Televisa’s outputs to 3 and 3 increases
earnings from 16 each to 18 each.
But TV Azteca cannot trust Televisa to collude since Televisa’s
best response to TV Azteca’s Q1 = 3 is Q2 = 4, not 3. And
Televisa cannot trust TV Azteca to collude since TV Azteca’s
best response to Televisa’s Q2 = 3 is Q1 = 4, not 3.
Televisa
Azteca
1
3
4
1
10,10
24,8
28,7
3
8,24
18,18
20,15
BA 210 Lesson II.5 Simultaneous Quantity Competition
4
7,28
15,20
16,16
40
Example 6: Merging
Example 6: Merging
BA 210 Lesson II.5 Simultaneous Quantity Competition
41
Example 6: Merging
Question: The market for legal research consists of two firms:
LexisNexis and Westlaw. As a manager of LexisNexis, you hire
your researchers at the same time as Westlaw, and so your
simultaneously choose your profit-maximizing research output
levels in the market. Law firms consider the output by the two
research firms as perfect substitutes. The demand for legal
research is Q = 10 - P; LexisNexis’s unit costs are 1; Westlaw’s
unit costs are 2; and both firms separately produce either 1, 4, or
5 units.
Compute LexisNexis’s profit, and compute Westlaw’s profit.
Ignoring antitrust law considerations, would it be profitable for
the two companies to merge? If so, compute the gains from a
merger. If the rules of bargaining allow LexisNexis’s to make a
take-it-or-leave-it offer to Westlaw, compute that offer.
BA 210 Lesson II.5 Simultaneous Quantity Competition
42
Example 6: Merging
Answer: You are Firm 1 in a Cournot Duopoly with demand Q =
10 - P, inverse demand P = 10-(Q1+Q2), unit costs c1 = 1 and c2
= 2, and alternative quantities Q1=1,4,5 and Q2=1,4,5.
Find the Nash Equilibrium solutions and dominance solutions to
the Cournot Duopoly Game (which turns out to be the dominance
solution), and compare the recommended solution to the
monopoly solution.
BA 210 Lesson II.5 Simultaneous Quantity Competition
43
Example 6: Merging
Compute the payoff table and Nash equilibrium for inverse
demand P = 10- (Q1+Q2), and unit costs c1 = 1 and c2 = 2: There
is more than one Nash equilibrium but the only dominance
solution (both eliminate 5, Lexis eliminates 1, Westlaw
eliminates 4) is LexisNexis chooses 4 and Westlaw chooses 1,
and so LexisNexis earns 16 and Westlaw earns 3.
Westlaw
Lexis
1
4
5
1
7,6
16,3
15,2
4
4,12
4,0
0,-4
BA 210 Lesson II.5 Simultaneous Quantity Competition
5
3,10
0,-5
-5,-10
44
Example 6: Merging
The monopoly solution for inverse demand P = 10- (Q1+Q2), has
each firm using the lowest unit costs, c1 = 1 and c2 = 1.
Recompute the payoff table and determine which cell maximizes
total profit. If either LexisNexis chooses 4 and Westlaw chooses
1 or LexisNexis chooses 1 and Westlaw chooses 4, then total
profit is maximized at 20.
Westlaw
Lexis
1
4
5
1
7,7
16,4
15,3
4
4,16
4,4
0,0
BA 210 Lesson II.5 Simultaneous Quantity Competition
5
3,15
0,0
-5,-5
45
Example 6: Merging
Merging thus increases total profit from P1+P2 = 16 + 3 = 19 to
P = 20, an increase of 1. So, 1 is the gains from a merger. If the
rules of bargaining allow LexisNexis to make a take-it-or-leave-it
offer to Westlaw, that offer should be 3 plus a pittance.
BA 210 Lesson II.5 Simultaneous Quantity Competition
46
Summary
Summary
BA 210 Lesson II.5 Simultaneous Quantity Competition
47
Summary
Payoff table entry to any Duopoly Game with inverse demand P
= a - bQ and constant unit costs c1 and c2:
• P = a - b(Q1+Q2)
• Firm 1 profit P1 = (P - c1) Q1
• Firm 2 profit P2 = (P - c2) Q2
BA 210 Lesson II.5 Simultaneous Quantity Competition
48
Review Questions
Review Questions
 You should try to answer some of the following questions
before the next class.
 You will not turn in your answers, but students may request
to discuss their answers to begin the next class.
 Your upcoming Exam 2 and cumulative Final Exam will
contain some similar questions, so you should eventually
consider every review question before taking your exams.
BA 210 Lesson II.5 Simultaneous Quantity Competition
49
BA 210
Introduction to Microeconomics
End of Lesson II.5
BA 210 Lesson II.5 Simultaneous Quantity Competition
50