1. There are two gas stations in town A, Al’s (“row” player) and Bob’s (“column” player). If both charge high prices, both make $5K per week. If both charge low prices, both make $3K per week. If one charges high prices and one charges low prices, the one that charges high prices makes nothing, and the one that charges low prices makes $6K per week. At the start of each week, both stores independently set their prices for the week. We will consider three possible strategies for each store: H: Always charge high prices. L: Always charge low prices. T: Tit-for-tat. Charge high prices the first week. The next week, do whatever the other store did the previous week. 
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3. 1) Construct the payoff matrix assuming that the two gas stations compete over a period of two weeks. 
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5. 2) Suppose the T strategy was not available to either player. Explain why the remaining 2 × 2 games would be a “Prisoner’s Dilemma” game. 
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7. 3) Which of Al’s strategies are strictly dominant? 
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9. 4) Which of Al’s strategies are weakly dominant and weakly dominated? 
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11. 5) Try to use iterated deletion of weakly dominated strategies (IDWDS) and find the Nash equilibrium. How far do you get? 
12. 6) Find all Nash equilibria of the game.

Answer rating: 100% (QA)

1 Construct the payoff matrix assuming that the two gas stations compete over a period of two weeks AlsBobs HL0 6K5K 0 LH6K 00 5K LL3K 3K3K 3K HH5K 5K... View the full answer