Worlds War 1

After having watched season 1 of The Expanse, I have been thinking that the interplanetary conflict between integrated world polities would not be the likely future.  Putting forth a purely hypothetical model, 4 or 5 or even 6 Great Power blocs on Earth would set about setting up largely independent (from each other) settlements on any future planetary bodies, the Outer Space Treaty notwithstanding.  To illustrate, a parallel can be drawn between the unfolding of the European dominance of the rest of the world over the last 500 years.  Projecting forward 500 years, we can model that the colonization of the Solar system to follow the roughly 3 phases much as European powers had taken over much of the world over the last half millennium..

Much of these phases overlap as many outposts had been established by the Europeans across the world.  The first object of Great Space Rivalry will be the Moon and control of cislunar space.  Similarly, the Americas became the first major colonial possession of European powers in the 16th and 17th centuries.  Spain and Portugal had a century jump on other powers, but others such as England, France, and Netherlands got their own later on. 

The powers had many trade routes and outposts developed in Asia.  Similarly, outposts of human colonies will be established relatively soon on the inner planets.  But much of the rivalry will focus on lunar space until it shifts to the other inner systems as those systems become more developed.

Scramble for the Gas Giants? 

The third major phase was subjugation of much of Africa by European empires.  Seeking resources, the Outer planets would eventually be "expropriated" for use by the inner colonies and Earth.  By this time or even before, new "nations" derived from the inner planet settlements will seek independence from their mother (Earth) countries.  Some of these may become great powers in their own right and join with the other great powers to get their own piece of the solar system pie.  To be sure, there will be outposts in the Outer System much earlier, but won't be much contended until developed to a certain 'saturation' level. 

Interstate rivals, Worlds Wars
As each celestial body would be split up by the Great Space powers, each colony would affect the balance of power in the planetary system and also balance among the Powers in the solar system. 
As each is first to the Moon, Mars, etc., it will induce efforts from rivals to establish their own colonies on the moon, mars and so forth.
So when would the first "worlds war" happen?  It will be from the result of rivalry over resources and 'prime locations' on the Moon.  In the first years of the 18th century, one of the first world wars (as counted by historians) was the War of the Spanish Succession. This war was fought by many  European power across several continents.  In much the same way, a future Worlds War would be fought by the Major Space Powers across several planetary fronts.