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.