Question

Consider a two-player game between Child’s Play and Kid’s Korner, each of which produces and sells wooden swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. The game is given as below:

Kid’s korner |
|||

High price |
Low price |
||

Child’s play |
High price |
64, 64 |
20, 72 |

Low price |
72, 20 |
57, 57 |

a. Suppose the players meet and make price decisions only once.
What is the Nash equilibrium in pure strategy of the game? (10
pts)

b. **Suppose this stage game is repeatedly
forever**. Let each of the two firms use a grim trigger
strategy in which they both price high unless one of them
“defects”, in which case they price low for the rest of the game.
Find the range of values of the discount factor, for which this
strategy is able to sustain cooperation in every period between the
two firms. (10 pts)

Answer #1

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Below is a game between player A and player B. Each player has
two possible strategies: 1 or 2. The payoffs for each combination
of strategies between A and B are in the bracket. For example, if A
plays 1 and B plays 1, the payoff for A is 1 and the payoff for B
is 0.
Player B
Strategy 1
Strategy 2
Player A
Strategy 1
(1,0)
(0,1)
Strategy 2
(0,1)
(1,0)
How many pure strategy Nash equilibria does...

Below is a game between player A and player B. Each player has
two possible strategies: 1 or 2. The payoffs for each combination
of strategies between A and B are in the bracket. For example, if A
plays 1 and B plays 1, the payoff for A is 1 and the payoff for B
is 0. Player B Strategy 1 Strategy 2 Player A Strategy 1 (1,0)
(0,1) Strategy 2 (0,1) (1,0) How many pure strategy Nash equilibria
does...

QUESTION 3
Below is a game between player A and player B. Each player has
two possible strategies: 1 or 2. The payoffs for each combination
of strategies between A and B are in the bracket. For example, if A
plays 1 and B plays 1, the payoff for A is -3 and the payoff for B
is -2.
Player B
Strategy 1
Strategy 2
Player A
Strategy 1
(-3,-2)
(10,0)
Strategy 2
(0,8)
(0,0)
How many pure strategy Nash...

2. Consider a market with two horizontally differentiated firms,
X and Y. Each has a constant marginal cost of $10. Demand functions
are: Qx = 100 –2Px + Py Qy = 100 –2Py + Px Suppose the two firms
are infinitely lived and have a discount factor of δ. Write down a
trigger strategy that could make cooperation sustainable on a
collusive price of 60 in an infinitely repeated duopoly game in the
above model. What is the condition on...

The average consumer of fine wine has a monthly demand curve for
wine which can be represented as P=44-2Q where Q is the number of
bottles of wine purchased in a month. The marginal cost for
WineWarehouse.com to sell a bottle of wine is MC=20. Provide a
graph to go along with your analysis.
For what discount rates would the firms be able to sustain this
collusion in an infinitely repeated game if they each play a grim
trigger (Nash...

Which of the following is true for a Nash equilibrium of a
two-player game?
a) The joint payoffs of the two players are highest compared to
other strategy pairs.
b) It is a combination of strategies that are best responses to
each other.*?
c) Every two-player game has a unique Nash equilibrium.
d) None of the above is correct.

Consider the following two-player game. Each player takes turns
placing a penny on the surface of a rectangular table. No penny can
touch a penny that is already on the table. The table starts out
with no pennies. The last player who makes a legal move wins. What
is the first player’s winning strategy?

Consider the scenario where two teams are looking to trade. The
acquiring team can offer a high price or a low price. The trading
team can offer a high quality player or a low quality player - the
acquiring team can't differentiate between these player types
before the trade is completed, though they can figure it out
later.
The table reflects the payoffs to each strategy for each
team.
Offer High Price
Offer Low Price
Trade High Quality Player
200,000...

Two firms play the game below. Each must choose strategy 1 or 2.
They choose their strategies simultaneously and without cooperating
with each other. Firm A?'s payoffs
are on the left side of each? cell, and
Firm B?'s payoffs are on the
right.
Firm A
Firm B
Strategy 1
Strategy 2
Strategy 1
10, 16
8, 12
Strategy 2
13, 12
17, 10
Determine the dominant strategy for each firm.
1) For Firm A :
A. Strategy 1 is a...

Consider the following simultaneous-move, one-shot game facing
two firms (Firm A and Firm B), with the payoffs given in Table I.
Assume the firms are not able to coordinate or communicate. Firm A
and B each has three strategic options.
Table I
Firm B
Firm A
Strategy
Low
average
high
Small
100, 125
300, 200
200, 190
Medium
250, 0
470, 340
480, 300
Large
300, -100
450, 450
475, 360
(a). For each of the firms, identify the dominant...

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