business, giving high-volume producers lower average cost in the future); compatibility (should AMD try to mimic Intel's chips or differentiate in some way?) Question 3: Lowest price guaranteed Two rms compete in prices. Each rm can set a high price or a low price. Prots as a function of prices are given by the following payoff matrix, where the rst value is Firm 1's prot, the second value Firm 2's prot: Firm 2 . Low High Low 70,70 120,0 Firm 1 , High 0,120 100,100 (a) Are there dominant strategies? What is the Nash Equilibrium of the game (if any)? Suppose now that each rm offers its customers a "lowest price guarantee:" if rm 2 offers a price lower than rm 1, then rm 1's customers are entitled to buy from rm 1 at the same price, even if rm 1 had initially set a high price; and similarly for firm 2's customers if rm 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 so on.) (b) How do lowest price guarantees change the game? (e) What is the equilibrium of the new game? What lessons can we learn? Answer: Problem Set 1 (Solutions) Page 3 (a) The only NE (in dominant strategies) is (Low,Low) The new game will look as follows: Firm 2 Low High Low 70,70 70,70 Firm 1 High 70,70 100,100 Now there is a second NE, which is (High,High). The presence of the guarantee allows to reach higher prots as it erases the incentive to charge a low price if the opponent charges a high price (as the opponent will meet the low price anyway)