Explain the ultimate defeat of the plains indians by whites

 1. Decline of the buffalo herds due to slaughter by white hunters for the pelts. 
2. Settlement of former Indian lands by homesteaders which reduced the ability of tribes to migrate freely through the plains. 
3. Hostile encounters with the US Army which provided a few victories for the Indians but the steady loss of Indian population reduced warriors to the point where they were consistently out manned and could not launch major campaigns. 

All three worked in concert but the loss of their major food source--the buffalo was the most damaging. Indians counted upon the buffalo for food and clothing. The plains were never conducive to an agrarian lifestyle for Indians and the loss of migrating buffalo herds sealed their doom.