This paper gives a sufficient condition on a bargaining region \(S\) for the Nash bargaining solution to coincide with the Rawlsian solution (i.e., \(\hbox{Max}_{u\in S}\min(u_ 1,u_ 2))\), where a threat point is assumed to be normalized to \((0,0)\). It is a degeneracy condition, and, of course, is rarely satisfied by a bargaining game.