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Homework answers / question archive / The next 3 questions involve the following game

The next 3 questions involve the following game

Economics

The next 3 questions involve the following game. There are two players, a husband and wife. They can either be selfish (S) or selfless (U) in their marriage. If they choose to be selfish, then there is a negative 'guilt' payoff of g. The payoff matrix is below. Figure 1: The Marriage Game Wife S U S 10-9, 10-9 15-9, 2 Husband U 2, 15-9 12. 12 Number left (right) of comma refers to H's (W's) payoff. 23. Suppose that g=0. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S. S) and (U, U) (D) (U, U). 24. Suppose that g = 5. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 25. Suppose that g = 10. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 8

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The first term of each cell in the payoff matrix will give the payoff of the husband while the second term will give the payoff of the wife. We indicate the optimal choices by underlinning them.

The cell containing the two underlines will give us the pure strategy Nash Equilibrium of the game.

1. The payoff matrix when g=0 is :

  Wife    
Husband   S U
  S 10 , 10 15 , 2
  U 2 , 15 12 , 12

(S,S) is the pure strategy Nash Equilibrium of this game.

Option A is the correct option for this answer.

2. The pay-off matrix when g=5 is :

  Wife    
Husband   S U
  S 5 , 5 10 , 2
  U 2 , 10 12 , 12

(S,S) and (U,U) are the pure strategy Nash Equilibria of the game.

Option C is the correct option.

3. The payoff matrix when g=10 is :

  Wife    
Husband   S U
  S 0 , 0 5 , 2
  U 2 , 5 12 , 12

(U,U) is the pure strategy Nash Equilibrium.

Option D is the correct option for this answer.

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