(a) Let G, G and G3 be the following games. Colin A Rose B A (10,3)...

 

Transcribed Image Text:

(a) Let G₁, G₂ and G3 be the following games. Colin A Rose B A (10,3) (7,5) (6,6) (8,4) G₁ Rose Rose Colin A Colin A B A (5,8) (4.2) B (9.2) (3,5) G₂ B A (4,4) (3,6) B (5.3) (2.7) G3 Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution. (b) Two companies produce similar items for the same market. Company 1 produces 91 items and Company 2 produces 92 items. The costs, C₁ and C₂, incurred by Company 1 and Company 2, respectively, are given by C₁ = aq₁ and C₂ = aq₂. and the market price P is given by P = A-91-92, where a and A are positive real numbers with a < A. Let ₁ and ₂ denote the profit made by Company 1 and Company 2, respectively. Both companies want to choose their production strategies in order to maximize their respective profits. (i) Find expressions for ₁ and ₂ in terms of q. 92. a and A. (ii) Find the solution of this problem using the Cournot model, giving your answers in terms of a and A. (iii) Find the solution of this problem using the Stackelberg model with Company 1 deciding its production strategy first, giving your answers in terms of a and A. (iv) Which of the two solutions would Company 1 prefer? Justify your answer. (a) Let G₁, G₂ and G3 be the following games. Colin A Rose B A (10,3) (7,5) (6,6) (8,4) G₁ Rose Rose Colin A Colin A B A (5,8) (4.2) B (9.2) (3,5) G₂ B A (4,4) (3,6) B (5.3) (2.7) G3 Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution. (b) Two companies produce similar items for the same market. Company 1 produces 91 items and Company 2 produces 92 items. The costs, C₁ and C₂, incurred by Company 1 and Company 2, respectively, are given by C₁ = aq₁ and C₂ = aq₂. and the market price P is given by P = A-91-92, where a and A are positive real numbers with a < A. Let ₁ and ₂ denote the profit made by Company 1 and Company 2, respectively. Both companies want to choose their production strategies in order to maximize their respective profits. (i) Find expressions for ₁ and ₂ in terms of q. 92. a and A. (ii) Find the solution of this problem using the Cournot model, giving your answers in terms of a and A. (iii) Find the solution of this problem using the Stackelberg model with Company 1 deciding its production strategy first, giving your answers in terms of a and A. (iv) Which of the two solutions would Company 1 prefer? Justify your answer.

Answer rating: 100% (QA)

a The game tree for G3 is as follows Rose 3 0 Colin Rose Colin Colin 1 2 A B A B 22 13 54 42 Using b... View the full answer