Question

2. YUM! Brands, Inc., based in Louisville, Kentucky, offers a diverse portfolio of “family style” restaurant concepts that do not serve alcoholic beverages, including: KFC, Pizza Hut, and Taco Bell, among others. AFC Enterprises, Inc., based in Atlanta, Georgia, is a big competitor. AFC offers spicy fried chicken under popular Popeyes Chicken & Biscuits brand. Suppose YUM! and AFC are contemplating entry into the rapidly-growing Austin, Texas, market. Both companies are considering three alternative restaurant formats to focus their efforts on one of three popular meal times: “Breakfast”, “Lunch”, or “Dinner”. The potential number of meals served per month for these three restaurant formats are 25,000 (breakfast), 62,500 (lunch), and 37,500 (dinner). If the two restaurant chains choose the same format, they will split the market for that format equally. If the two restaurant chains choose different formats, each will get the total potential market for that format. Assume that profit payoff are proportionate to the number of meals served, so the meals served numbers can suffice as inputs to the payoff matrix. The first number in the payoff matrix is the number of meals served by YUM! Brands; the second number is the number of meals served by AFC Enterprises. Find the Nash equilibria in this problem. Does the presence of multiple Nash equilibria pose coordination problems in arriving at a point of Nash equilibrium? Explain.

AFC Enterprises Breakfast Lunch Dinner YUM! Brands Breakfast 12,500; 12,500 25,000; 62,500 25,000; 37,500 Lunch 62,500; 25,000 31,250; 31,250 62,500; 37,500 Dinner 37,500; 25,000 37,500; 62,500 18,750: 18,750