(3) Black Friday [Past exam question] C&M Electronics and 8th Street Photo are two retailers that have been competing with one another for many years. Every year, both retailers hold a major one-day sale on the Friday after Thanksgiving. Local residents know about this sale and plan their holiday electronics shopping around this event. Historically, both C&M and 8th Street have chosen a 10%, 20%, or 30% off sale. The amount of the sale can differ across the two stores, and both stores keep their own sale amount a tightly guarded secret until a public announcement in the Thanksgiving edition of the Daily Times, the local newspaper. Since residents base their shopping decisions on what they read in the paper and only visit one store on Friday, neither C&M nor 8th Street find it profitable to change their sale amounts after the newspaper has been printed. You are advising C&M Electronics, and they have provided you the profits (in $'000s) that C&M expects each firm to receive for any combination of sale amounts announced. They are uncertain about certain numbers in the matrix, which they have replaced with X and Y. 8th Street Photo 10% 20% 30% 10% 50, Y 40, 30 20, 15 C&M 20% 60, 20 45, 25 25, 15 Electronics 30% 47, 5 35, X 30, 10 (a) What is the highest value of X such that it is a Nash equilibrium for both firms to choose 30% discounts? (Provide one number; if no such number exists, write "N/A".) Explain. (b) What is the lowest value of Y such that it is a Nash equilibrium for both firms to choose 10% discounts? (Provide one number; if no such number exists, write "N/A".) Explain. For parts (c) through (g), assume that X = 15 and Y = 35 in the payoff matrix above. (c) Does either firm have any dominated strategies? If so, list them. Explain your answer. (d) What is the Nash equilibrium in this game, and what are its corresponding payoffs? Explain your answer. This year, C&M is thinking about running an early advertising campaign announcing its discount before the Thanksgiving Day newspaper is printed (and before 8th Street Photo chooses its own discount). You are certain 8th Street Photo is not planning an early announcement of its own, and you have also received credible information that 8th Street will not choose 30%. (e) Draw the game tree for the new game in which C&M Electronics announces its discount first and then 8th Street Photo chooses either a 10% or 20% discount. What is the equilibrium of this new game, and what are its payoffs? Be sure to explain your answer. (f) What is the most C&M would pay to run its early advertising campaign? Explain. (g) How do you think 8th Street Photo will respond in future years? Why