Ch10_Q&A

1 Chapter 10 Game Theory -- Suggested Questions Question 1 Consider a pricing game for GPUs between two firms: Nvidia and AMD. The payoff represents the total profits for each firm per period in millions of dollars. AMD Strategy Hold Prices Cut Prices Nvidia Hold Prices 24, 24 19, 25 Cut Prices 26, 20 22, 21 (a) Determine Nvidia ’s dominant strategy. (b) Determine AMD ’s dominant strategy. (c) Determine the dominant-strategy equilibrium. (d) What strategy is the best-response for Nvidia? (e) What strategy is the best-response for AMD? (f) Determine the Nash equilibrium of this game. (g) Do the characteristics of a Prisoner’s Dilemma apply to this game ? Solution: (a) Nvidia ’s dominant st rategy is to choose “ Cut Prices. ” (b) AMD ’s dominant st rategy is to choose “ Cut Prices. ” (c) The dominant-strategy equilibrium is (Cut Prices, Cut Prices). (d) Nvidia ’s best -response strategy is to choose “ Cut Prices. ” (e) AMD ’s best -response strategy is to choose “ Cut Prices. ” (f) The Nash equilibrium is (Cut Prices, Cut Prices). (g) Yes. The alternative outcome (Hold Prices, Hold Prices) is better than the Nash Equilibrium (Cut Prices, Cut Prices).

2 Question 2 Consider the following game in a matrix form with two players. Player 2 Strategy C D Player 1 A 5, 8 30, 15 B 10, 20 40, 22 (a) Determine Player 1’s dominant strategy. (b) Determine Player 2’s dominant strategy. (c) Determine the dominant-strategy equilibrium. (d) What strategy is Player 1’s b est-response? (e) What strategy is Player 2’s best-response? (f) Determine the Nash equilibrium of this game. (g) Do the characteristics of a Prisoner’s Dilemma apply to this game ? Solution: (a) Player 1’s dominant st rategy is B. (b) Player 2’s dominant st rategy is D. (c) The dominant-strategy equilibrium is (B, D) (d) Player 1’s best response strategy is B. (e) Player 1’s best response strategy is D. (f) Nash equilibrium is (B, D) (g) No.

4 Question 4 Consider the following game. Two players, Taylor and Olivia, must decide whether to reveal the coin as Heads or Tails. They then simultaneously make their choices known. If the coins match – either both Heads or both Tails – Taylor receives $1 and Olivia forfeits $1. However, if the coins do not match – one shows Heads and the other shows Tails – Olivia gains $1 and Taylor loses $1. Olivia Strategy Heads Tails Taylor Heads 1, -1 -1, 1 Tails -1, 1 1, -1 (a) Determine Taylor 1’s dominant strategy. (b) Determine Olivia 2’s dominant strategy. (c) Determine the dominant-strategy equilibrium. (d) What strategy is Taylor ’s best -response strategy? (e) What strategy is Olivia ’s best -response strategy? (f) Determine the Nash equilibrium of this game. (g) Do the characteristics of a Prisoner’s Dilemma apply to this game?

5 Solution: (a) There is no dominant strategy for Taylor. (b) Olivia does not have a dominant strategy. (c) Since neither player has a dominant strategy, there is no dominant-strategy equilibrium. (d) Taylor's best-response strategy depends on Olivia's choice. • If Olivia chooses "Heads," Taylor's best-response strategy is to choose "Heads." • If Olivia chooses "Tails," Taylor's best-response strategy is to choose "Tails." (e) Olivia's best-response strategy depends on Taylor's choice. • If Taylor chooses "Heads," Olivia's best-response strategy is to choose "Tails." • If Taylor chooses "Tails," Olivia's best-response strategy is to choose "Heads." (f) There is no Nash equilibrium. (g) No.

7 Question 6 Consider the game below: Player C Strategy C1 Strategy C2 Player R Strategy R1 600, 600 100, 1000 Strategy R2 1000, 100 200, 200 (a) Does each firm have a strictly dominant strategy? (b) Determine the best-response strategy of each player. (c) Determine the dominant strategy equilibrium. (d) Determine the Nash equilibrium. (e) Is this an example of P risoner’ s dilemma game? Solution: (a) Yes. • R2 is strictly dominant strategies of Player R. • C2 is strictly dominant strategies of Player C. (b) Player R’s best - response strategy is R2. Player C’s best -response strategy is C2. (c) A dominant-strategy equilibrium is (R2, C2). (d) A Nash equilibrium is (R2, C2). (e) Yes. It is an example of Prisoner’ s dilemma game since there is a payoff (600, 600) better than the Nash equilibrium.