All of them wanted to control the area so that they could exclusively exploit the lucrative fur trade there.
This was the major reason that the French and British wanted to build forts at the confluence of the Allegheny and Monongahela rivers, and it was this that led to the French and Indian War (began 1754).
The Native Americans obtained valuable trade goods (particularly tools,weapons, and ironware made from steel and other metals) for furs, so also had a strong interest in controlling the area themselves.