Question

In the “divide two apples” game, player 1 suggests a division scheme (x,y) from the set {(2, 0), (1, 1), (0, 2)} where x is the number of apples allocated to player 1, and y is the number of apples allocated to player 2. Player 2 counters with a division scheme of her own that comes from the same set. The final allocation is obtained by averaging the two proposed division schemes. The apples can be cut if the resulting numbers are fractional. The payoff of each player is the number of apples (possibly fractional) he or she receives.

a) How many pure strategies does either player have?

b) Find the pure strategy subgame-perfect equilibria of this
game.

c) Find all pure strategy Nash equilibria of this game that are not
subgame-perfect.

Answer #1

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...

Consider the following game. Player 1’s payoffs are listed
first, in bold:
Player 2
X
Y
Player 1
U
100 , 6
800 , 4
M
0 , 0
200 , 1
D
10 , 20
20 , 20
Imagine that Player 1 makes a decision first and Player 2 makes
a decision after observing Player 1’s choice. Write down every
subgame-perfect Nash equilibrium of this game.
Does the outcome above differ from the Nash equilibrium (if the
game...

The next two questions will refer to the following game
table:
Player 2
X
Y
A
2, 3
6, 1
Player 1
B
4, 2
1, 3
C
3, 1
2, 4
Question1
Which of Player 1's pure strategies is non-rationalizable,
in a mixed-strategy context?
Group of answer choices
A
B
C
Question2
Using your answer to the previous question, find all of this
game's mixed-strategy Nash equilibria.
*If you used graphs to help you answer the previous question and...

There are two players. First, Player 1 chooses Yes or
No. If Player 1 chooses No, the game ends and
each player gets a payoff of 1.5. If Player 1 chooses Yes,
then the following simultaneous-move battle of the sexes game is
played:
Player 2
O
F
Player 1
O
(2,1)
(0,0)
F
(0,0)
(1,2)
Using backward induction to find the Mixed-Strategy
Subgame-Perfect Equilibrium.

(4) In this game, each of two players can volunteer some of
their spare time planting and cleaning up the community garden.
They both like a nicer garden and the garden is nicer if they
volunteer more time to work on it. However, each would rather that
the other person do the volunteering. Suppose that each player can
volunteer 0, 1, 2, 3, or4 hours. If player 1 volunteers x hours and
2 volunteers y hours, then the resultant garden...

Consider a modified sequential
version of Paper Scissors Rock where Player 1 goes first and
chooses Paper, Scissors or Rock, and Player 2 goes second and
chooses Paper, Scissors, or Rock. For each player, a win gets a
payoff of 1, a loss gets a payoff of -1, and a tie get a payoff of
0.
(a) (9 points)
Write out the entire game tree for this sequential game.
(b) (4 points) Find all the subgame perfect equilibria using
backwards...

Two players can name a positive integer number from 1 to 6. If
the sum of the two numbers does not exceed 6 each player obtains
payoff equal to the number that the player named. If the sum
exceeds 6, the player who named the lower number obtains the payoff
equal to that number and the other player obtains a payoff equal to
the difference between 6 and the lower number. If the sum exceeds 6
and both numbers are...

Consider the following
2 period sequential game. There are two players,
Firm 1 and Firm 2. They pro- duce identical goods and these goods
are perfect substitutes. The inverse demand function in this market
is given by P = 12 − (q1 + q2).
Firm 1 moves first and choose its output q1. Firm 2
observes Firm 1’s decision of q1 and then
chooses its output q2.\
Suppose that the cost function of both Firm 1 and 2 is given...

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