Wonders of world

I like the idea of a mmo Civilization. But since Civ is built as a singel player game and have monopoly of a wonder gives most players a huge dissadvantage towards those who gets ahead in the game in a mmo version of the game. Why not let all be able to build them but only the first gets on the wonder of the world list. Everyone else that builds it after the first only gets a reduced one of the original wonder and is not shown in the list.