I don't know anything about the video game market, but I doubt that buying up a company that I've never heard of would make EA a monopoly. As for not improving the product, that's their business decision.
Oh, and they DID compete for the business--they competed to get that exclusive contract.
Actually they didn't. The NFL has no intention of going exclusive until the enormous offer from EA was made. Then NFL did the smart thing and tried to turn it into a bidding war to see how much money it could make by announcing their willingness to go exclusive.
The size of the offer that EA made was at that time larger then any exclusive contract every paid to league for exclusive rights. EA was well aware that no other company could match it. The NFL went to take 2 and said can you beat it. The obvious answer was no. Take 2 didn't have the financial resources at the time to beat that offer. You can't call that competition.
Also, anybody who loved video game football knew both Madden and the 2K franchise. NFL2K franchise had been beating Madden in reviews for several years. Madden was losing face and losing market share every year. Plus you had the 2k folks advertising their number one rated football game every year.
I don't blame EA though for doing what they could. If you can't beat the competition....eliminate the competition. It's a smart business move.
Many in the industry called it horrible for fans and and predicated EA would have little incentive to innovate or improve the franchise. Unfortunately, they were correct.
Average Rankings (Based on the number 1 selling console at the time)
NFL2k - 91%
Madden - 86.4%
NFL2K2 - 84.7%
Madden 02 - 80%
NFL2k3 - 89.9%
Madden 03 - 89.6% (lower but considered rebound year)
ESPN NFL Football (NFL2K4) - 89.4%
Madden 04 - 88.5%
ESPN NFL2K5 - 90%
Madden 05 - 89.6%
The disparity between the scores of other consoles and the PC was even worse. Clearly 2K had the upper hand with critics and was making a better product then EA.