Aspartame is a low-calorie sweetener marketed by Monsanto under the name of NutraSweet. It was a major impetus to the rapid growth of Diet Coke and Diet Pepsi during the 1980s and 1990s. Holland Sweetener was quite optimistic about capturing a large share of the US market. To Holland Sweetener\'s surprise, they never became a big player in the US market. Coke and Pepsi signed long-term contracts with Monsanto for the continued supply of NutraSweet. The big winners in this contract negotiation were Coke and Pepsi who realized about $200 million a year in savings. Monsanto remained the major supplier to these companies, while Holland Sweetener was "left pretty much out in the cold"

Envision a pricing problem between Monsanto and Holland Sweetener that led to the Monsanto contract. Assume (1) the cost to Holland Sweetener of entering the US market is $25 million; (2) Monsanto and Holland Sweetener simultaneously choose to quote either a high or low price to Pepsi and Coke for aspartame; (3) if both Monsanto and Holland Sweetener quote the same price, Pepsi and Coke contract with Monsanto because customers are familiar with the NutraSweet label-Holland Sweetener loses its initial investment; (4) if both firms submit a high price, Monsanto nets $300 million; (5) if both firms submit a low price, Monsanto nets $100 million; (6) if Monsanto prices high and Holland Sweetener prices low, Holland Sweetener nets $100 million (after the initial investment) and Monsanto nets $0; (7) if Monsanto prices low and Holland Sweetener prices high Monsanto nets $100 million and Holland Sweetener loses its investment.

A. Construct the payoff matrix for this strategic pricing problem. Find the Nash equilibrium.

B. Now assume that eh interaction is sequential where Holland Sweetener chooses to enter and if so they face the pricing problem in the second stage.  Should Holland Sweetener enter?