Positive affine invariance in bargaining
= Positive affine invariance in bargaining
{title2=$u_i\mapsto a_i u_i+b_i,\quad a_i>0$}
Transforming each utility by an independent positive affine map must transform the chosen payoff by the same map. The <Nash product> changes only by a positive factor, so the <Nash bargaining solution> has this invariance.