the new capitalism

(This is a previous post renamed.) So the Cold War was over and democratic capitalism defeated communism (=1 party dictatorship +socialism).  All the world (almost) is clamoring into developing capitalism.  Is there any reason to believe that our version of capitalism will continue to be dominant or even successful in this new world?  I hear a lot about China not playing by the rules (trade and environmental) and a new state capitalism.  I'll bet the Chinese believe that they have just as much right as anyone else to write the rules.  Remember, there is no referee.