Question 1

The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A)run to the right side with probability .71.
B)run to the right side with probability .83.
C)be sure to run to the right side.
D)run to the two sides with equal probability.
E)run to the right side with probability .60.

Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, Michigan's optimal strategy involves mixing between running left and right in such a way that the opponent is indifferent between defending left or right. Given the information, if Michigan runs right, they have a 0.60 chance of gaining at least 5 yards even if the opponent defends right. To make the opponent indifferent, the probability of running right (p) must be such that the expected gain from defending either side is equal. If Michigan runs left and the opponent defends left, Michigan gains nothing. If Michigan runs right and the opponent defends right, Michigan still has a 0.60 chance of gaining 5 yards. The opponent will mix their defense strategy to make Michigan indifferent between running left or right, leading to a situation where Michigan's probability of choosing right maximizes their minimum guaranteed gain, which is achieved by running to the right side with a probability of 0.71, making the opponent indifferent and establishing a Nash equilibrium.

Question 2

Two players are engaged in a game of &#34;chicken.&#34; There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called &#34;chicken&#34; and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 4 if the other player Swerves and a payoff of -36 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and&#10;A)a mixed strategy equilibrium in which one player swerves with probability 0.90 and the other swerves with probability 0.10.&#10;B)a mixed strategy in which each player swerves with probability 0.45 and drives straight with probability 0.55.&#10;C)a mixed strategy equilibrium in which each player swerves with probability 0.90 and drives straight with probability 0.10.&#10;D)two mixed strategies in which players alternate between swerving and driving straight.&#10;E)no mixed strategies.

Accepted Answer

The only mixed strategy that can be an equilibrium is one in which both players are indifferent between swerving and driving straight. This means that both players would have the same expected payoff from each strategy, and therefore would be willing to play either one with equal probability. Since the payoff for swerving is always zero, this means that both players would only want to swerve if the expected payoff for driving straight is lower than zero. Using the payoff formula, we can set up the following equation:

4p + (F1F1F1S1-F1F1F1036)(1-p) = 0

where p is the probability that each player will choose to drive straight. Solving for p, we get:

p = (F1F1F1S1-F1F1F1036)/4

This means that both players would choose to drive straight with probability (F1F1F1S1-F1F1F1036)/4 and swerve with probability 1 - (F1F1F1S1-F1F1F1036)/4 = (16-F1F1F1S1+F1F1F1036)/4. Since both players would have the same strategy, this is a mixed strategy equilibrium.

We can also check that this equilibrium is stable by verifying that neither player can gain by deviating from their strategy. If a player were to change their strategy, they would have to either increase their probability of driving straight or decrease it. If they increase their probability, their expected payoff would also increase, but if they decrease it, their expected payoff would decrease. Therefore, each player's strategy is optimal given the other player's strategy, and this is a Nash equilibrium.

Question 3

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait, both get 1.If both pigs Press the Button, then Big Pig gets 6 and Little Pig gets 4.If Little Pig Presses the Button and Big Pig Waits at the Trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig Presses the Button and Little Pig Waits, then Big Pig gets 6 and Little Pig gets 2.In Nash equilibrium,

A)Little Pig will get a payoff of 4 and Big Pig will get a payoff of 6.
B)Little Pig will get a payoff of 2 and Big Pig will get a payoff of 6.
C)both pigs will wait at the trough.
D)Little Pig will get a payoff of zero.
E)the pigs must be using mixed strategies.

Accepted Answer

the pigs must be using mixed strategies.

Question 4

The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A)run to the right side with probability .71.
B)run to the right side with probability .83.
C)be sure to run to the right side.
D)run to the two sides with equal probability.
E)run to the right side with probability .60.

Accepted Answer

In a Nash equilibrium, both the offense and defense adjust their strategies based on the other's actions to reach a point where neither can benefit by changing their strategy unilaterally. Given Michigan's higher probability of gaining at least 5 yards when running to the right (.70) even if the defense also focuses on the right, the offense is incentivized to favor the right side. However, to prevent the defense from always defending the right, Michigan must mix its strategy to keep the defense guessing. The exact probability of .77 for choosing the right side is calculated based on the game's specific payoffs and the need to make the defense indifferent between defending left or right, leading to a mixed strategy Nash equilibrium.

Question 5

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait, both get 1.If both pigs Press the Button, then Big Pig gets 6 and Little Pig gets 4.If Little Pig Presses the Button and Big Pig Waits at the Trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig Presses the Button and Little Pig Waits, then Big Pig gets 6 and Little Pig gets 2.In Nash equilibrium,

A)Little Pig will get a payoff of 4 and Big Pig will get a payoff of 6.
B)Little Pig will get a payoff of 2 and Big Pig will get a payoff of 6.
C)both pigs will wait at the trough.
D)Little Pig will get a payoff of zero.
E)the pigs must be using mixed strategies.

Accepted Answer

In Nash equilibrium, each player chooses the strategy that maximizes their payoff given the other player's strategy. If Big Pig waits at the trough, Little Pig's best strategy is to Press the Button since she gets a payoff of 1 instead of 0. If Little Pig Presses the Button, Big Pig's best strategy is to Press the Button as well, since he gets a higher payoff of 5 instead of 0. Therefore, the strategy profile (Press the Button, Waits at the Trough) is a Nash equilibrium, where Big Pig's payoff is 5 and Little Pig's payoff is 1.

Question 6

Two players are engaged in a game of &#34;chicken.&#34; There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called &#34;chicken&#34; and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 84 if the other player Swerves and a payoff of -36 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and&#10;A)a mixed strategy equilibrium in which each player swerves with probability 0.30 and drives straight with probability 0.70.&#10;B)two mixed strategies in which players alternate between swerving and driving straight.&#10;C)a mixed strategy equilibrium in which one player swerves with probability 0.30 and the other swerves with probability 0.70.&#10;D)a mixed strategy in which each player swerves with probability 0.15 and drives straight with probability 0.85.&#10;E)no mixed strategies.

Accepted Answer

CIn a mixed strategy Nash equilibrium for a game like "chicken," each player randomizes over their strategies in such a way that makes the other player indifferent between their own strategies. The probabilities given in choices A and C allow for such a scenario, where the expected payoffs from swerving and driving straight can be equalized for both players, depending on the specific payoffs of the game.

Question 7

Two players are engaged in a game of &#34;chicken.&#34; There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called &#34;chicken&#34; and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 15.43 if the other player Swerves and a payoff of -36 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and&#10;A)two mixed strategies in which players alternate between swerving and driving straight.&#10;B)a mixed strategy in which each player swerves with probability 0.35 and drives straight with probability 0.65.&#10;C)a mixed strategy equilibrium in which one player swerves with probability 0.70 and the other swerves with probability 0.30.&#10;D)a mixed strategy equilibrium in which each player swerves with probability 0.70 and drives straight with probability 0.30.&#10;E)no mixed strategies.

Accepted Answer

The payoff matrix for the game is:
\begin{array}{c|cc} & Swerve & Drive Straight \ \hline Swerve & 0, 0 & 15.43, F1F1F1S1-F1F1F1036 \ Drive Straight &F1F1F1S1-F1F1F1036 , 15.43 & 15.43, 15.43 \end{array}
For there to be a mixed strategy equilibrium, the players must be indifferent between Swerve and Drive Straight. This means that the expected payoff for each player must be the same for both strategies. Let p be the probability that Player 1 chooses Drive Straight and q be the probability that Player 2 chooses Drive Straight. Then the expected payoffs are:

For Player 1:
\begin{aligned} 0p+(F1F1F1S1-F1F1F1036)(1-p)&=15.43p+15.43(1-p)\ (F1F1F1S1-F1F1F1036)+1036p-1036p&=15.43+15.43p-15.43p\ F1F1F1S1&=15.43 \end{aligned}
This equation has no solution, so there is no mixed strategy equilibrium in which both players choose Drive Straight with positive probability.

For Player 2:
\begin{aligned} 0q+(F1F1F1S1-F1F1F1036)(1-q)&=15.43q+15.43(1-q)\ (F1F1F1S1-F1F1F1036)+1036q-1036q&=15.43+15.43q-15.43q\ F1F1F1S1&=15.43 \end{aligned}
This equation also has no solution, so there is no mixed strategy equilibrium in which both players choose Drive Straight with positive probability.

Therefore, the only possibility is that one player chooses Swerve and the other player chooses Drive Straight with positive probability. Let p be the probability that Player 1 chooses Swerve and q be the probability that Player 2 chooses Swerve. Then the expected payoffs are:

For Player 1:
\begin{aligned} 0p+(F1F1F1S1-F1F1F1036)(1-p)&=15.43q+0(1-q)\ (F1F1F1S1-F1F1F1036)+1036p-1036p&=15.43q\ F1F1F1S1-F1F1F1036&=15.43q\ q&=\frac{F1F1F1S1-F1F1F1036}{15.43} \end{aligned}
For Player 2:
\begin{aligned} 0q+(F1F1F1S1-F1F1F1036)(1-q)&=15.43p+0(1-p)\ (F1F1F1S1-F1F1F1036)+1036q-1036q&=15.43p\ F1F1F1S1-F1F1F1036&=15.43p\ p&=\frac{F1F1F1S1-F1F1F1036}{15.43} \end{aligned}
Since F1F1F1S1>F1F1F1036, both probabilities are greater than zero. Therefore, a mixed strategy equilibrium is:
Answer: D
 Both players swerve with probability 0.70 and drive straight with probability 0.30.

Question 8

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait, both get 1.If both pigs Press the Button, then Big Pig gets 6 and Little Pig gets 4.If Little Pig Presses the Button and Big Pig Waits at the Trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig Presses the Button and Little Pig Waits, then Big Pig gets 6 and Little Pig gets 2.In Nash equilibrium,

A)Little Pig will get a payoff of 4 and Big Pig will get a payoff of 6.
B)Little Pig will get a payoff of 2 and Big Pig will get a payoff of 6.
C)both pigs will wait at the trough.
D)Little Pig will get a payoff of zero.
E)the pigs must be using mixed strategies.

Accepted Answer

In Nash equilibrium, both pigs will choose the strategy that maximizes their payoff given the strategy chosen by the other pig. In this case, both pigs will choose to Wait at the Trough, as this gives them both a payoff of 4, which is higher than the payoff they would get from any other strategy.

Question 9

The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A)run to the right side with probability .71.
B)run to the right side with probability .83.
C)be sure to run to the right side.
D)run to the two sides with equal probability.
E)run to the right side with probability .60.

Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Let $ p $ be the probability that Michigan runs to the right, and $ 1-p $ the probability they run to the left. The defense will choose to defend the right with probability $ q $ and the left with probability $ 1-q $. For Michigan to be indifferent between running left or right, the expected gain from both must be equal. If Michigan runs right, the expected gain is $ 0.7 \times 5q + 5(1-q) = 3.5q + 5 - 5q = 5 - 1.5q $. If Michigan runs left, the expected gain when the defense guesses wrong is 5, which happens with probability $ q $, so the gain is $ 5q $. Setting these equal to make Michigan indifferent: $ 5 - 1.5q = 5q $ leads to $ 6.5q = 5 $, so $ q = \frac{5}{6.5} = \frac{10}{13} $. Since the defense is also indifferent, Michigan's probability $ p $ of running right should make the defense's expected loss the same whether they defend left or right, leading to the same calculation for $ p $. Thus, Michigan runs to the right with probability $ \frac{10}{13} $, which is approximately 0.77.

Question 10

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait, both get 1.If both pigs Press the Button, then Big Pig gets 6 and Little Pig gets 4.If Little Pig Presses the Button and Big Pig Waits at the Trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig Presses the Button and Little Pig Waits, then Big Pig gets 6 and Little Pig gets 2.In Nash equilibrium,

A)Little Pig will get a payoff of 4 and Big Pig will get a payoff of 6.
B)Little Pig will get a payoff of 2 and Big Pig will get a payoff of 6.
C)both pigs will wait at the trough.
D)Little Pig will get a payoff of zero.
E)the pigs must be using mixed strategies.

Accepted Answer

In Nash equilibrium, each player's strategy is the best response to the other player's strategy. Here, if Little Pig chooses to Wait, Big Pig's best response is to Press the Button, resulting in a payoff of 4 for Big Pig and 1 for Little Pig. This outcome is stable because neither pig has an incentive to deviate from their chosen strategy, given the strategy of the other.

Question 11

Two players are engaged in a game of &#34;chicken.&#34; There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called &#34;chicken&#34; and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 3 if the other player Swerves and a payoff of -12 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and&#10;A)a mixed strategy equilibrium in which each player swerves with probability 0.80 and drives straight with probability 0.20.&#10;B)a mixed strategy equilibrium in which one player swerves with probability 0.80 and the other swerves with probability 0.20.&#10;C)a mixed strategy in which each player swerves with probability 0.40 and drives straight with probability 0.60.&#10;D)two mixed strategies in which players alternate between swerving and driving straight.&#10;E)no mixed strategies.

Accepted Answer

The answer of Two players are engaged in a game...

Question 12

Arthur and Bertha are asked by their boss to vote on a company policy.Each of them will be allowed to vote for one of three possible policies, A, B, and C.Arthur likes A best, B second best, and C least.Bertha likes B best, A second best, and C least.The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $3.The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1.The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for.If Arthur and Bertha vote for different outcomes, the boss will pick C.Arthur and Bertha know this is the case.They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B.What is the mixed strategy equilibrium for Arthur and Bertha in this game?

A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
B)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
C)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
D)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
E)Arthur votes for A and Bertha votes for B.

Accepted Answer

The answer of Arthur and Bertha are asked by their...

Question 13

Two players are engaged in a game of &#34;chicken.&#34; There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called &#34;chicken&#34; and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 48 if the other player Swerves and a payoff of -48 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and&#10;A)a mixed strategy equilibrium in which each player swerves with probability 0.50 and drives straight with probability 0.50.&#10;B)a mixed strategy in which each player swerves with probability 0.25 and drives straight with probability 0.75.&#10;C)a mixed strategy equilibrium in which one player swerves with probability 0.50 and the other swerves with probability 0.50.&#10;D)two mixed strategies in which players alternate between swerving and driving straight.&#10;E)no mixed strategies.

Accepted Answer

The answer of Two players are engaged in a game...

Question 14

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait, both get 1.If both pigs Press the Button, then Big Pig gets 6 and Little Pig gets 4.If Little Pig Presses the Button and Big Pig Waits at the Trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig Presses the Button and Little Pig Waits, then Big Pig gets 6 and Little Pig gets 2.In Nash equilibrium,

A)Little Pig will get a payoff of 4 and Big Pig will get a payoff of 6.
B)Little Pig will get a payoff of 2 and Big Pig will get a payoff of 6.
C)both pigs will wait at the trough.
D)Little Pig will get a payoff of zero.
E)the pigs must be using mixed strategies.

Accepted Answer

The answer of Big Pig and Little Pig have two...

Question 15

Arthur and Bertha are asked by their boss to vote on a company policy.Each of them will be allowed to vote for one of three possible policies, A, B, and C.Arthur likes A best, B second best, and C least.Bertha likes B best, A second best, and C least.The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $3.The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1.The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for.If Arthur and Bertha vote for different outcomes, the boss will pick C.Arthur and Bertha know this is the case.They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B.What is the mixed strategy equilibrium for Arthur and Bertha in this game?

A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
B)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
C)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
D)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
E)Arthur votes for A and Bertha votes for B.

Accepted Answer

The answer of Arthur and Bertha are asked by their...

Question 16

Arthur and Bertha are asked by their boss to vote on a company policy.Each of them will be allowed to vote for one of three possible policies, A, B, and C.Arthur likes A best, B second best, and C least.Bertha likes B best, A second best, and C least.The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $3.The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1.The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for.If Arthur and Bertha vote for different outcomes, the boss will pick C.Arthur and Bertha know this is the case.They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B.What is the mixed strategy equilibrium for Arthur and Bertha in this game?

A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
B)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
C)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
D)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
E)Arthur votes for A and Bertha votes for B.

Accepted Answer

The answer of Arthur and Bertha are asked by their...

Question 17

Arthur and Bertha are asked by their boss to vote on a company policy.Each of them will be allowed to vote for one of three possible policies, A, B, and C.Arthur likes A best, B second best, and C least.Bertha likes B best, A second best, and C least.The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $3.The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1.The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for.If Arthur and Bertha vote for different outcomes, the boss will pick C.Arthur and Bertha know this is the case.They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B.What is the mixed strategy equilibrium for Arthur and Bertha in this game?

A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
B)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
C)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
D)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
E)Arthur votes for A and Bertha votes for B.

Accepted Answer

The answer of Arthur and Bertha are asked by their...

Question 18

The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A)run to the right side with probability .71.
B)run to the right side with probability .83.
C)be sure to run to the right side.
D)run to the two sides with equal probability.
E)run to the right side with probability .60.

Accepted Answer

The answer of The old Michigan football coach had only...

Question 19

The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A)run to the right side with probability .71.
B)run to the right side with probability .83.
C)be sure to run to the right side.
D)run to the two sides with equal probability.
E)run to the right side with probability .60.

Accepted Answer

The answer of The old Michigan football coach had only...

Question 20

Arthur and Bertha are asked by their boss to vote on a company policy.Each of them will be allowed to vote for one of three possible policies, A, B, and C.Arthur likes A best, B second best, and C least.Bertha likes B best, A second best, and C least.The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $3.The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1.The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for.If Arthur and Bertha vote for different outcomes, the boss will pick C.Arthur and Bertha know this is the case.They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B.What is the mixed strategy equilibrium for Arthur and Bertha in this game?

A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
B)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
C)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
D)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
E)Arthur votes for A and Bertha votes for B.

Accepted Answer

The answer of Arthur and Bertha are asked by their...

Question 21

Suppose that in the Hawk-Dove , the payoff to each player is -7 if both play Hawk.If both play Dove, the payoff to each player is 4, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 7 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A).08.
B).30.
C).65.
D).15.
E)1.

Accepted Answer

The answer of Suppose that in the Hawk-Dove , the...

Question 22

Suppose that in the Hawk-Dove game , the payoff to each player is -7 if both play Hawk.If both play Dove, the payoff to each player is 5, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 9 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A).36.
B).68.
C).09.
D).18.
E)1.

Accepted Answer

The answer of Suppose that in the Hawk-Dove game ,...

Question 23

Suppose that in the Hawk-Dove game , the payoff to each player is -7 if both play Hawk.If both play Dove, the payoff to each player is 5, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 9 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A).36.
B).68.
C).09.
D).18.
E)1.

Accepted Answer

The answer of Suppose that in the Hawk-Dove game ,...

Question 24

Suppose that in the Hawk-Dove game the payoff to each player is -8 if both play Hawk.If both play Dove, the payoff to each player is 3, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 8 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A).19.
B).69.
C).38.
D).10.
E)1

Accepted Answer

The answer of Suppose that in the Hawk-Dove game the...

Question 25

Suppose that in the Hawk-Dove game , the payoff to each player is -7 if both play Hawk.If both play Dove, the payoff to each player is 5, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 9 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A).36.
B).68.
C).09.
D).18.
E)1.

Accepted Answer

The answer of Suppose that in the Hawk-Dove game ,...

Deck 30: Extension: A: Game Applications