Consider a game between Alice and Bob. Alice and Bob are firms producing widgets and competing in prices. Their constant marginal costs are equal to zero. There are ten consumers, each of whom values their products at $5. The consumers will buy a product from whichever firm sells the product at the lowest price. If both firms sell at the same price, then 5 consumers will buy from one firm, and the other 5 will buy from the other firm. 1. Assume that the price-setting game is played in only one period and that Alice and Bob can each choose any price p e R4. Find all pure strategy Nash equilibrium(s) of this game. 2. Assume that Alice and Bob repeatedly play this game for ten periods. Continue assuming that they can each choose any price p e R4. Which per-period prices are possible in at least one subgame-perfect equilibrium? Describe the strategy profiles which can sustain such prices in words. 3. Now assume that the price-setting game is played in only one period and that Alice and Bob can each choose any price p E 0,1,2,3,4,5}. Find all pure strategy Nash equilibrium(s) of this game. 4. Assume that Alice and Bob repeatedly play this game for 10 periods. Continue assuming that they can each choose any price p e {0,1,2,3,4,5}. Which per-period prices are possible in at least one subgame-perfect equilibrium? Describe the strategy profiles which can sustain such prices in words.