Pure strategy Nash quilibria.

Question

The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.

Answer 1

Question

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

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The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.

Suppose two players play a two-period repeated game, where the stage game is the normal-form game shown below. Is there a subgame perfect Nash equilibrium in which the players select (A, X) in the first period? If so, fully describe such equilibrium. If not, explain why not. Player 1 has choice A, B; Player 2 has choice X, Y, Z. Payoff: (A,X)-(5,7), (A,Y)-(2,4), (A,Z)-(3,8), (B,X)-(1,4), (B,Y)-(3,5), (B,Z)-(1,4)

Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote, and determine the Nash Equilibrium.

Answer 2

Question

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Expert Solution & Answer

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Answer 3

Question

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Expert Solution & Answer

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Answer 4

Question

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Expert Solution & Answer

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Answer 5

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Answer 6

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

Answer 7

Chapter 17, Problem 17.3P

a

To determine

Pure strategy Nash quilibria.

Answer 8

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

Answer 9

b)

To determine

Pure strategy Nsh equilibria when players prefer fairness

Answer 10

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Answer 11

c)

To determine

Pure strategy Nash equilibria when new preferences are made.

Answer 12

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Ch. 17.3 - Prob. 1MQ Ch. 17.3 - Prob. 2MQ Ch. 17.3 - Prob. 1.1MQ Ch. 17.3 - Prob. 1.2MQ Ch. 17.3 - Prob. 2.2MQ Ch. 17.3 - Prob. 1.3MQ Ch. 17.3 - Prob. 1TTA Ch. 17.3 - Prob. 2TTA Ch. 17.4 - Prob. 1TTA Ch. 17.4 - Prob. 2TTA

Pure strategy Nash quilibria.

Solution Summary: The author explains that in a pure strategy involving single action, the Nash equilibrium is such that no player has the incentive to deviate from the equilibrium.

Pure strategy Nash quilibria.

Pure strategy Nsh equilibria when players prefer fairness

Pure strategy Nash equilibria when new preferences are made.

Chapter 17 Solutions