1. A simultaneous move game. Use the following game to answer the questions below: L C R T 100, 125 300, 250 200, 100 M 250, 0 500. 500 750, 400 B 0. -100 400, 300 -100, 350 (a) Find each player's dominant strategy, if it exists. (b) Find the Nash equilibrium. 2. Intel and AMD. The following normal form game depicts the pricing rivalry between Intel and AMD for their newest top-of-the-line chip. Each company considers five possible price levels: $449, $399, 8349, $299 and $249. Monthly profits in million dollars are: AMD 419 309 349 209 249 449 200, 50 180, 70 150, 55 120, 45 95, 30 399 230, 35 210, 45 160, 50 130, 40 110, 25 Intel 349 210, 15 190, 25 180, 30 140, 35 120, 20 299 180, 5 170, 15 150, 20 120, 25 100, 15 249 120, -5 110, 10 105, 15 95, 20 90, 10 (a) Find each firm's best response to each possible strategy of the other. (b) What is (are) the Nash equilibrium (equilibria) of the game? (c) What combination of strategies generates the highest total profit? Why might the two firms not be able to come to an agreement on this outcome? (d) What aspects do you think are left out in this game? (This is an open question; please limit your answer to a paragraph or two.) 3. Lowest price guarantee. Two firms compete in prices. Each firm can set a high price or a low price. Profits as a function of prices are given by the following payoff matrix, where the first value is Firm I's profit, the second value Firm 2's profit: Firm 2 Low High Firm ] Low 70, 70 120, 0 High 0. 120 100, 100 (a) Are there dominant strategies? What is the Nash Equilibrium of the game (if any)? Suppose now that each firm offers its customers a "lowest price guarantee:" if firm 2 offers a price lower than firm 1, then firm I's customers are entitled to buy from firm 1 at the same price, even if firm I had initially set a high price; and similarly for firm 2's customers if firm 1 offers a price lower than firm 2. Lowest price guarantees are common in many markets, including sporting goods, books, housewares, cellular phones, electronics, luggage and travel accessories, toys, tires, eyewear, prescription drugs, and 80 on.) (b) How do lowest price guarantees change the game? (c) What is the equilibrium of the new game? What lessons can we learn