Are the Yankees a Monopoly?

My question to everyone is, are the Yankees a monopoly? Yes, I know that in class we covered that there are really no monopolies in the everyday world. However, I want to ask, are the Yankees a monopoly in the baseball world? With peeking the payroll records every year now for the last ten, the Yankees have done nothing but buy the best players and gather up the best records in baseball. Yes it is true that they lost to the Boston Red Sox this past world series, but still we all know that George Stienbrener will come back next season with something up his sleeve.
My next question is about one of the aspects we covered in class relating to a monopolist. That is price discrimination. In my mind the Yankees have handed over these huge contracts and made impressions on these players that they are worth these ridiculous amounts. I know as a Cleveland fan that the Indians not only would never pay A-Rod the money hes making, but couldn't afford it to begin with. With that in mind is it really fair? The Yankee's can afford to pay these top players what ever they want and with the game of baseball turing into a money game we know noone will beat out the Yankees eventually in this money game.
Finally, I would like to bring up the dead weight loss side to this possable monopoly. Do you think that by the Yankees having all the top players have hurt and cost other franchises money? Of course. Every year you can pencil them in as a playoff spot, meaning that that other teams that couldnt afford to keep up with the Yanks are left to a loss in not only the extra money the playoffs bring to a team but the social aspect as well.
In closing I just wanted to point out that in recognition of the free market world of baseball the Yankees are becoming a monpolist. Should the government put a salary cap on baseball, or should we let these monopolist bore up the amercain past time.