To save face is an important part of Oriental culture, as harmony is regarded as the key to accomplishing anything and everything socially. Here , I am talking about face-saving not only for an individual but for people he is dealing with as well.
To this end, usually a compromise is reached so everyone is happy. But, if that’s not the case, try to agree to disagree graciously and leave the back-door open and, above all, make sure you do not embarrass the other party especially in public.
This is something you’d better master in daily life, business and otherwise.