Globalism means more and more kinds of competition are removed as regulation is removed. For example, look at the coordination between the major central banks across the world. Also, monopolies prevail.
Yes on that scale, but as regulations are removed, competition on a more micro level is booming.
Although we see today somewhat institutional monopolies I wouldn't like to predict how long those will last and how long they will be stable especially since it's a complex system. We are, after all, only beginning globalisation (in the sense of collective global system coordination) and will probably (re)discover new mechanisms along the way.