Why did European nations agree to follow the Open Door policy proposed by the U.S?

Most scholars believe that the Open Door policy that the
US proposed had very little impact on anything.  The European nations never really
agreed to it in any formal way.  To the extent that the  European nations agreed to the
policy, they did so because it was a way of reducing conflict between
them.

During the early part of the 1900s, the major
European nations had more to worry about than spheres of influence in China.  World War
I was rapidly approaching and European nations were more concerned with affairs closer
to home, both in Europe and in Africa.  Because of this, it was not worth their while to
come into conflict with the US or with each other by trying to expand their control over
"their" parts of China.

So, when the European nations eemed
to be agreeing to the Open Door policy (and remember, they never did so formally), it
was because it was in their interests to reduce conflict in China so they could
concentrate on the problems brewing in other, more important, areas of the
world.