The Mishna says that when 3 people eat together they are obligated to make a zimun for birchas hamazon and are not allowed to bentch individually. The gemara discusses whether 2 people are not obligated in zimun but may still do zimun if they wish, or whether the entire concept of zimun was only instituted for a group of 3. We pasken that with less than 3 people zimun cannot be done, as the gemara proves from R. Yochanan who says that with 2 people eating together one can be yotzei with the bracha of the other. Rashi explains that the concept of one being yotzei with the others bracha implies that we are not using the concept of zimun, because with zimun we view it as if each person is making their own bracha. The gemara also explains that this bidieved approach of one person being motzi another in birchas hamazon only applies when the listener is a boor and unable to make birchas hamazon himself, but if he is able to make birchas hamazon himself, he is obligated to do so. Even when the listener is a boor, the M.B. (193:5) cites two opinions whether the listener can be yotzei in lashon hakodesh when he doesn't understand lashon hakodesh.
Why is it that the Rabbonon were so much more stringent about birchas hamazon than they were about hamotzi? When it comes to the bracha of hamotzi one person is able to make a bracha for another even lichatchila (so long as they are koveia themselves together, as we do every shabbos), but for birchas hamazon, unless there are 3 and an obligation to make a mezuman, ideally each must bentch themself. Why?
Tosafos (d.h. im ratzu) explains that when it comes to bracha rishona they are coming together as a group to do things together, but when it comes to a bracha achrona when their intention is to break as a group and depart from one another, one cannot be motzi another unless there is a zimun. Tosafos offers another approach that birchas hamazon which is d'oraysa they were more machmir for than bracha rishona which is only d'rabonon. The difference between these two approaches is for one to be motzi another in a regular bracha achrona such as borei nefashos or bracha achas me'ein shalosh. According to the first approach of Tosafos, one cannot be motzi another in any bracha achrona unless the listener is unable to make a bracha himself, whereas according to the second approach, since bracha achas me'ein shalosh according to most opinions is only d'rabonon (not like rabban gamliel), one can be motzi another. The Pri Megadim understands that another difference would be when one at less than a כדי שביעה of bread. According to the first opinion someone else cannot be motzi him, but according to the second opinion someone else can be motzi him since he is only obligated m'drabonon.
Regarding an obligation to make a zimun when there are 3 people, the Bach writes that even on shivas haminin there may be an obligation for zimun, therefore 3 people should not eat together any of the shivas haminin since it will be questionable whether they require zimun. The M.B. (193:6) cites the Birkei Yosef who disagrees and says that only on bread is there an obligation of zimun.