Coke and Pepsi each choose one of two prices: "Low" (P = $2) or "High" (P = $3). There are 50 buyers who will pick the lowest price option. However, if the prices are the same, 25 will buy from Coke and 25 from Pepsi. For simplicity, assume there are no costs, so profit is just price times quantity. a. Draw the 2x2 payoff matrix and find Nash equilibrium.
b. Now assume that each company has 20 loyal buyers who buy their brand regardless of price. This leaves 10 non-loyal buyers that pick the less expensive option. Again, non-loyal buyers split evenly if the prices are the same. Draw the new payoff matrix and find Nash equilibrium.