Consider the following game: (7,3) and P1 (4,5) b (3,6) Suppose each player has Fehr-Schmidt preferences....

 

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Consider the following game: (7,3) and P1 (4,5) b (3,6) Suppose each player has Fehr-Schmidt preferences. So, for an outcome (1, 2), we have U₁(1, ₂) = 21-a₁ max{2x₁,0} - 3₁ max{₁x2,0} P2 U₂(1,2)=x2-a2 max{1x2,0} - 3₂ max{2x1,0} Throughout this problem, assume 32 > 1/1. (a) Compute U₂(4, 5) and U₂(3, 6). Which action will P2 choose at their decision node? (b) Compute U₁(7,3) and U₁(4, 5). Under what condition will P1 prefer outcome (4,5) over (7,3)? (The condition is an inequality involving a₁ and 3₁). (c) The Fehr-Schmidt model assumes 0 ≤ 3 < 1 and a; 23; for each player i. Under these assumptions, will P1 prefer (4,5) over (7,3)? (d) Suppose we drop the requirement that a; 23₁. In particular, let a₁ = and 3₁ = 1/2 Find the subgame perfect Nash equilibrium of the game, and provide some intuition for the result (a few sentences should suffice). Consider the following game: (7,3) and P1 (4,5) b (3,6) Suppose each player has Fehr-Schmidt preferences. So, for an outcome (1, 2), we have U₁(1, ₂) = 21-a₁ max{2x₁,0} - 3₁ max{₁x2,0} P2 U₂(1,2)=x2-a2 max{1x2,0} - 3₂ max{2x1,0} Throughout this problem, assume 32 > 1/1. (a) Compute U₂(4, 5) and U₂(3, 6). Which action will P2 choose at their decision node? (b) Compute U₁(7,3) and U₁(4, 5). Under what condition will P1 prefer outcome (4,5) over (7,3)? (The condition is an inequality involving a₁ and 3₁). (c) The Fehr-Schmidt model assumes 0 ≤ 3 < 1 and a; 23; for each player i. Under these assumptions, will P1 prefer (4,5) over (7,3)? (d) Suppose we drop the requirement that a; 23₁. In particular, let a₁ = and 3₁ = 1/2 Find the subgame perfect Nash equilibrium of the game, and provide some intuition for the result (a few sentences should suffice).

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