ESSEC Business School_ECOI 31143: Business Economics Midterm Exam. Questions & Solutions.

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ESSEC Business School_ECOI 31143: Business Economics Midterm Exam. Questions & Solutions. Question 1 There are two high-tech firms (F1 and F2 respectively) in an industry. Each firm needs to decide ... on the standards to adopt for its operating system. There are two possible standards, A and B, and the two firms simultaneously and independently decide on their standard. If both firms adopt standard A, the profits of F1 and F2 are 10 and 8 respectively. If both firms adopt standard B, the profits of F1 and F2 are 6 and 9 respectively. If F1 adopts standard A and F2 standard B, the profits of F1 and F2 are 3 and 2 respectively. If F1 adopts standard B and F2 standard A, both firms earn zero profits. 1. Represent the game the two firms play in a matrix where F1 selects rows and F2 selects columns. (2p) Answer. F1 F2 A B A 10,8 3,2 B 0,0 6,9 2. Do firms have strictly dominated actions? If yes, eliminate them. (1p) Answer. There are no strictly dominated action for any of the players. For F1, A is best if F2 plays A and B is best if F2 plays B. Similarly for F2. 3. Find all the pure and mixed strategy Nash equilibria of the game. (2p) Answer. There are two pure strategy Nash equilibria: (A; A) and (B; B). Below, the BRs of F1 are depicted by lower bars and the BRs of F2 are depicted by upper bars. F1 F2 A B A 10; 8 3,2 B 0,0 6; 9 ESSEC Business School page 2 of 10Business Economics Midterm Exam Fall 2020 In addition to the two pure strategy equilibria, there is also an equilibrium in mixed strategies. To find this suppose that F1 plays A w.p. q1 and F2 plays A w.p. q2. The payoffs of F1 from playing A and B are respectively U1(A) = 10q2 + 3(1 − q2) = 3 + 7q2 U1(B) = 0q2 + 6(1 − q2) = 6 − 6q2 In a mixed strategy equilibrium, F1 is indifferent between all the undominated actions. Therefore U1(A) = U1(B) , 3 + 7q2 = 6 − 6q2 , q2∗ = 3 13 The payoffs of F2 from playing A and B are respectively U2(A) = 8q2 + 0(1 − q2) = 8q2 U2(B) = 2q2 + 9(1 − q2) = 9 − 7q2 In a mixed strategy equilibrium, F2 is indifferent between all the undominated actions. Therefore U2(A) = U2(B) , 8q2 = 9 − 7q2 , q1∗ = 3 5 Therefore, in the mixed-strategy equilibrium, F1 plays A w.p. 3=5 and F2 plays A w.p. 3=13. 4. Depict the best responses of the two firms in a graph in which the horizontal axis represents the probability that F1 plays A and the vertical axis represents the probability that F2 plays A. (1p) ESSEC Business School page 3 of 10Business Economics Midterm Exam Fall 2020 Answer. The blue line is the BR of F1 and the red line is the BR of F2. We know from above that when q1 = 3=5, F2 is indifferent between A and B; for q1 > 3=5, F2 strictly prefers A to B; and for q1 < 3=5, F2 strictly prefers B to A. This is how the BR of F2 is constructed. The BR of F1 is constructed in a similar way [Show More]

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