Question

- Two firms operating in the same market must choose between a high price and a low price. In the payoff matrix below, Firm A's profit is listed before the comma, B's profit is listed after the comma. The firms are playing a one-period (“one shot”) simultaneous game.

Firm B |
|||||

High Price |
Low Price |
||||

Firm A |
High Price |
40,40 |
18,50 |
||

Low Price |
50,18 |
25,25 |
|||

- State whether each firm does or does not have a dominant strategy. No explanation is necessary – you need only clearly indicate your answer

- Is the above game a Prisoners’ Dilemma? Briefly explain why or why not.

Answer #1

A) A dominant strategy for a firm is the strategy that makes the firm better off always regardless of what it's opponent chooses.

Firm A's Dominant strategy is 'low price' because Matter what firm B chooses, firm A is always better off by choosing low price.

Firm B's dominant strategy is also 'low price', because setting low price always earns firm B higher payoff.

B) A prisoner's dilemma is a game where two players acting strategically will ultimately result in a suboptimal equilibrium outcome. Communication between the two players can drastically alter their best strategies.

The given game is an example of prisoners dilemma, because when the two firms plays without cooperation, they both end up setting low price. But if they communicate, and choose high price, they could have earned higher payoff.

Two firms operating in the same market must choose between a
high price and a low price. In the payoff matrix below, Firm A's
profit is listed before the comma, B's profit is listed after the
comma. The firms are playing a one-period (“one shot”) simultaneous
game. Firm B High Price Low Price Firm A High Price 40,40 18,50 Low
Price 50,18 25,25 a. State whether each firm does or does not have
a dominant strategy. No explanation is necessary...

PAYOFF MATRIX FOR A PRICING GAME
FIRM B
Low Price
High Price
FIRM A
Low Price
(50,000; 50,000)
(80,000; 30,000)
High Price
(30,000; 80,000)
(20,000; 20,000)
From the above payoff matrix where the
payoffs are the profits of the two firms, determine whether:
Firm A has a dominant strategy. If so, what is
it?
Firm B has a dominant strategy. If so, what is it?
The optimal strategy for each firm if there is any.
Will a Nash equilibrium exist...

Two firms operate in the market for a certain hair care product.
If they both have a large advertising budget, they each earn profit
of $600. If they both have a low advertising budget, they each earn
profit of $400. If one firm has a large advertising budget and the
other low, then the high advertising firm earns profit of $700
while the low advertising firm earns profit of $200.
Write out the payoff matrix for this game.
Does either...

Using a payoff matrix to determine the equilibrium
outcome
Suppose there are only two firms that sell smart phones,
Flashfone and Pictech. The following payoff matrix shows the profit
(in millions of dollars) each company will earn, depending on
whether it sets a high or low price for its phones.
Pictech Pricing
High
Low
Flashfone Pricing
High
11, 11
2, 18
Low
18, 2
10, 10
For example, the lower, left cell shows that if Flashfone prices
low and Pictech...

6. Using a payoff matrix to determine the equilibrium
outcome
Suppose there are only two firms that sell tablets: Padmania and
Capturesque. The following payoff matrix shows the profit (in
millions of dollars) each company will earn, depending on whether
it sets a high or low price for its tablets.
Capturesque Pricing
High
Low
Padmania Pricing
High
11, 11
3, 20
Low
20, 3
10, 10
For example, the lower-left cell shows that if Padmania prices
low and Capturesque prices...

Refer to the normal-form game of price competition in the payoff
matrix below.
Firm B
Low Price
High Price
Firm A
Low Price
0, 0
50, -10
High Price
-10, 50
20, 20
If the low price / low price payoffs for both players are 30
(instead of 0), is this game a prisoners' dilemma?
A. YES
B. NO

1) Consider the following game in which two firms decide how
much of a homogeneous good to produce. The annual profit payoffs
for each firm are stated in the cell of the game matrix, and Firm
A's payoffs appear first in the payoff pairs: Firm B - low output
Firm B - high output Firm A - low output 300, 250 200, 100 Firm A -
high output 200, 75 75, 100
a. What are the dominant strategies in this...

column player
low price high
price
Row low price 0, 0 50,
-10
Player high price -10,
50 10, 10
The numbers in the matrix represent profit. The row
player has a dominant strategy of a low price (0 is better than -10
and 50 is better than 10) and the column player has a
dominant strategy of a low price as well (similar numbers). And,
low low is a Nash equilibrium.
A dilemma that arises here is that both could be better off if
they both went with...

Two firms must make pricing decisions without collusion. Profits
resulting from their decision are given in the following table:
Firm 1
High
Low
High 10,12 -2,18
Firm
2
Low
16,3
2,5
Explain the Nash equilibrium. Does this game have dominant
strategy equilibrium? Explain. Is this game a prisoner's dilemma?
Explain. Is there an advantage in moving first? Explain. What is
the cooperative solution?

Price competition between firms, from the firms’ perspective,
can be similar to the prisoners’ dilemma. The best outcome for all
firms would be for all to charge a high price. However, if the
other firms charge a high price, any individual firm has incentives
to charge a low price and steal the market. Additionally, if any
other firm chooses a low price, each firm should charge a low price
too so that it doesn’t get priced out of the market....

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