Question

Use the following information is answering questions 1 - 11. Assume the demand in a market is given by Q = 100 - 2P and that MC = AC = 10. Assume there are two sellers whose strategy is to choose a quantity and that seller 1 chooses first and seller 2 chooses second. Assume this game is repeated an infinite number of times.

1. The Stackelberg equilibrium in this market is for firm 1 to produce ____ and firm 2 to produce _____.

2. In the Stackelberg equilibrium, firm 1’s profit is _____ and firm 2’s profit is ______.

3. The monopoly output level in this market is ______.

4. If firm 1 promises to produce Q_{1} = 28 if firm 2
will produce Q_{2} = 12, firm 1 will earn profit equal to
______.

5. Firm 1’s gain in profit in this suggested collusive behavior is ______.

6. If firm 2 agrees to firm 1’s suggestion, firm 2’s profit is ______.

7. If firm 2 cheats and produces its profit maximizing level of
output instead, firm 2 would produce Q_{2} equal to
______.

8. If firm 2 cheats and produces its profit maximizing level of output instead, firm 2 would earn a profit equal to ______.

9. The one time gain in profit for firm 2 from cheating is equal to ______.

10. The loss in profit to firm 2 in each of the future periods because firm 2 cheats is _____.

11. Firm 2 would agree to the collusive suggestion of firm 1 as long as firm 2’s interest rate is less than ______.

Use the following information to answer questions 12 - 15.

Player 2

A B

A (3, 0) (2, -1)

Player 1

B (2, 8) (5, 3)

12. The unique Nash equilibrium in this game when it is played one time and the players choose simultaneously is ______.

13. Both players would prefer the strategy pair ______ to the Nash equilibrium.

14. When this game is repeated an infinite number of times, Player 1 would choose B when Player 2 chooses B if and only if Player 1’s rate of interest is less than _____.

15. When this game is repeated an infinite number of times, Player 2 would choose B when Player 1 chooses B if and only if Player 2’s rate of interest is less than _____.

Player 2

A B

A (3, 6) (-1, 2)

Player 1

B (6, 2) (0, 3)

Use the payoff matrix above for questions 16 - 18.

16. The unique Nash equilibrium in this game when it is played one time and the players choose simultaneously is ______.

a) (A, A)

b) (B, B)

c) (A, B)

d) (B, A)

e) there is no Nash equilibrium

17. When this game is repeated an infinite number of times, Player 1 would choose A when Player 2 chooses A if and only if Player 1’s rate of interest is less than _____.

a) 20%

b) can be any positive number

c) 50%

d) 60%

e) 30%

18. When this game is repeated an infinite number of times, Player 2 would choose A when Player 1 chooses A if and only if Player 2’s rate of interest is less than _____.

a) 20%

b) 40%

c) 60%

d) can be any positive number

e) 30%

Use the following information when answering questions 19 - 24. Assume that the reservation price for each buyer in a market is 10, and that there are 60 such buyers. Also assume that MC = AC = 6. Also assume that seller 1 and seller 2 each has a capacity of selling 50 units and that prices must be integers. Assume that if they charge the same price then they each sell half the quantity demanded. Assume the game is played one time.

19. If seller 1 chooses a price of 9, seller 2’s best response
is to choose P_{2} = _____.

a) 10

b) 6

c) 7

d) 8

e) 9

20. When sellers 1 and 2 each charge price equal to _____ , then we have a Bertrand/Nash equilibrium.

a) 8

b) 6

c) 9

d) 7

e) 10

21. In this Bertrand/Nash equilibrium, each seller earns a profit = _____.

a) 60

b) 40

c) 100

d) 80

e) 50

Use the following information in addition to that given above to answer questions 22 - 24. Assume the Bertrand game with capacity constraint is to be repeated an infinite number of times.

22. When each seller charges a price equal to 10, each earns a profit equal to ______.

a) 100

b) 140

c) 200

d) 120

e) 300

23. When one seller charges a price equal to 10 and the other cheats by choosing its best response, the cheating seller earns a profit equal to _____.

a) 120

b) 160

c) 150

d) 200

e) 180

24. The gain in profit from cheating rather than setting P = 10 is _____, and the loss in profit from having the Bertrand/Nash equilibrium rather than colluding and setting price equal to 10 is _____.

a) 50, 50

b) 40, 80

c) 60, 60

d) 60, 30

e) 30, 60

Answer #1

Consider the following prisoner’s dilemma
Player 1
Share
Fight
Share
15,15
5,18
Player
2
Fight
18,5
7,7
a. Identify each players Nash strategies.
b. Does this game have a Nash equilibrium? If yes what is it?
c. Does this game have dominant strategy equilibrium? If yes what
is it?
d What makes it a Prisoner’s dilemma?
e. What is the incentive to cheat?
f....

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2 Assume both firms are colluding to raise the equilibrium
price. If one firm defected from (i.e. broke) their agreement how
much would they earn? (Assume the game was played once.)
3 Now assume the game is infinitely repeated and the...

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2. Solve for the Cournot-Nash equilibrium.
3. Now assume this market has a Stackelberg leader, Firm 1.
Solve for the quantity, price, and profit for each firm.
4. Assume there is no product differentiation and the firms
follow a Bertrand pricing model. Solve for the...

Consider the two firms engaging in the Bertrand competition. On
the demand side the market demand equation is p=200-Q. Consumers
only buy from the firm charging the lower pric When charging the
same price, they share the market equally. On the supply side, they
have different marginal costs, with MC1=60 and MC2=50, and there is
no fixed cost. Find the market price and the winner’s profit at the
equilibrium.
a.
At the equilibrium the market price is 60 and the...

Assume there are two firms in a Stackelberg game. Firm 1 chooses
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firm has identical marginal cost of 100. Determine the Nash
equilibrium for this game.

1. Consider a market with inverse demand P (Q) = 100 Q and two
firms with cost function C(q) = 20q.
(A) Find the Stackelberg equilibrium outputs, price and total
profits (with firm 1 as the leader).
(B) Compare total profits, consumer surplus and social welfare
under Stackelberg and Cournot (just say which is bigger).
(C) Are the comparisons intuitively expected?
2. Consider the infinite repetition of the n-firm Bertrand game.
Find the set of discount factors for which full...

1. For the following payoff matrix, find these:
a) Nash equilibrium or Nash equilibria (if any)
b) Maximin equilibrium
c) Collusive equilibrium (also known as the "cooperative
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Firm A
Strategy X
Strategy Y
Firm B
Strategy X
200
23
250
20
Strategy Y
30
50
1
500
2. For the following payoff matrix, find these:
a) Nash equilibrium or Nash equilibria...

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enjoys a monopoly profit of 2 and firm 2 earns 0 profit. If firm 2
decides to enter the market, then firm 1 has two strtegies : either...

Suppose two oil-producing countries are interested in forming a
cartel with the goal of colluding -– an agreement to raise oil
prices (and profits) by limiting supply. Suppose, in each period,
simultaneously choose between their individual options: to collude
(Co) or to cheat (Ch) and over-produce, impacting the other
nation's revenues (shown in the following matrix)
country A Co 3,3 1,6,
Ch 6,1 2,2
a. What famous game format does this game follow (or what game
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Game Theory Econ
Imagine a market setting with three firms. Firms 2 and 3 are
already operating as monopolists in two different industries (they
are not competitors). Firm 1 must decide whether to enter
firm 2’s industry and thus compete with firm 2 or enter firm 3’s
industry and thus compete with firm 3. Production in firm 2’s
industry occurs at zero cost, whereas the cost of production in
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