It would depend on your definition of "Plains Game". If Eland or Roan are on the Menu, the requirements are a bit different from the smaller antelopes.
For the former I would suggest something with .300 in its title as a minimum.
For the others, the Old Man, my son and I used .223, 7x57, .300Win and .375. They all worked.

There is nothing made by man,
which cannot be broken by woman.