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# Use the following payoff matrix for a simultaneous-move one-

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Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 2
Strategy C D E F
Player 1 A 25, 15 4, 20 16, 14 28, 12
B 10, 10 5, 15 8, 6 18, 13
a. What is player 1's optimal strategy? Why?
b. Determine player 1's equilibrium payoff.

Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives \$0 and player 2 receives \$15. If both players move left, player 1 receives - \$10 and player 2 receives \$8. If player 1 moves left and player 2 moves right, player 1 receives 10 and player 2 receives \$10.
a. Write the above game in extensive form.
b. Find the ash equilibrium outcomes to this game.
c. Which of the equilibrium outcomes is most reasonable? Explain.

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#### Solution Preview

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 2
Strategy C D E F
Player 1 A 25, 15 4, 20 16, 14 28, 12
B 10, 10 5, 15 8, 6 18, 13
a. What is player 1's optimal strategy? ...

#### Solution Summary

Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 2
Strategy C D E F
Player 1 A 25, 15 4, 20 16, 14 28, 12
B 10, 10 5, 15 8, 6 18, 13
a. What is player 1's optimal strategy? Why?
b. Determine player 1's equilibrium payoff.

Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives \$0 and player 2 receives \$15. If both players move left, player 1 receives - \$10 and player 2 receives \$8. If player 1 moves left and player 2 moves right, player 1 receives 10 and player 2 receives \$10.
a. Write the above game in extensive form.
b. Find the ash equilibrium outcomes to this game.
c. Which of the equilibrium outcomes is most reasonable? Explain.

\$2.19

## Problem Set

1. Explain why personalized pricing or first degree price discrimination is usually more profitable than menu price. Why, if this is the case, do companies use menu pricing?

2. Companies often sell multiple products (e.g., such as PepsiCo produces and sells both soft drinks and snack foods such as Fritos and Lays potato chips). Discuss at least two ways that this strategy can increase value. What dimension it add to pricing strategies?

3. You are the manager of Copies R Us (CRU). The only other copy store in the immediate area is Carbon Copy (CC). CC is considering buying a color copier and offering color copying services. If CC buys the color copier, its profits will increase by \$1500 per year assuming CRU does not offer color copying services, while CRU's profits will decline by \$500 per year. If CRU also buys a color copier and offers color copying services, its profits will increase by \$500 per year and CC's profits also will increase by \$500 per year. If CRU decides to buy a copier and CC does not, CRU's profits will increase by \$1500 per year and CC's will fall by \$500.

a. Construct the strategic form payoff matrix assuming simultaneous move, non-repeated interaction.
b. Show the predicted outcome or equilibrium for this game.
c. Do either or both CC and CRU have dominant strategies? If so, what are they?
d. Construct a sequential, extensive form diagram assuming that CC moves first (Node 1) and CRU makes its decision after CC decides whether or not to buy the color copier. Does the outcome of this game change from the one you identified in part b?

4. Match the following statements with the four terms below. Explain your reasoning for matching the term with the statement.

Terms: