That depends on how optimized the AGI is for economic growth rate. Too poorly optimized and a more highly optimized fast-follower could eclipse it.

At some point, there will be an AGI with a head start that is also sufficiently close to optimal that no one else can realistically overtake its ability to simultaneously grow and suppress competitors. Many organisms in the biological world adopt the same strategy.

If they become self improving, the first one would outpace all the other AI labs and capture all the economical value.