Berachos, Chapter 6, Mishnah 6. This Mishnah addresses the question of when one person can fulfill the obligation of a berachah on behalf of his fellow diners, and when this is not possible.
"Hayu yoshvin le'echol" - eating without reclining:
"Hayu yoshvin le'echol - kol echad ve'echad mevarech le'atzmo" - If they were sitting to eat, each one recites the berachah for himself. Sitting down to eat, without reclining, indicates an informal meal. In the times of the Mishnah a formal meal always involved reclining, and so when people merely sit down to eat, there is no establishment of a meal. Since they are not sitting down together for a genuine meal, one person's berachah cannot fulfill the obligation of the others, and each one recites the berachah for himself.
"Heisevu" - an established meal:
"Heisevu - echad mevarech lechulan" - If they reclined, one recites the berachah for them all. In their times, reclining was the sign that those at the table were eating an established meal, and therefore one person can recite the berachah of Hamotzi and fulfill the obligation of the others.
Wine brought during the meal:
"Ba lahem yayin besoch hamazon - kol echad ve'echad mevarech le'atzmo" - If wine was brought to them in the middle of the meal, one person does not fulfill the obligation of his fellow; rather, each one recites the berachah for himself. It is worth knowing that if a person had not drunk wine beforehand, and the wine is brought in the middle of the meal, he must recite "Borei pri hagafen," and the bread does not exempt him from this berachah. Even so, under these circumstances each one recites his own berachah.
The Gemara explains the reason: "ein beis hablia panui" - a person's swallowing passage, the place where he swallows, is not free. Two explanations are offered for what this means:
Rashi: Those at the table are occupied with their eating, and their attention is not free to listen to the berachah.
Others explain: Since a person is in the middle of swallowing, he cannot answer amen; and if he does answer, there is even an element of danger involved, since he is liable to choke.
For this reason it was established that each one recites his own berachah.
Wine brought after the meal and the berachah on the mugmar:
"Le'achar hamazon - echad mevarech lechulam" - If the wine comes after the meal, before Bircas Hamazon, one person may already recite the berachah and fulfill the obligation of them all.
"Vehu omer al hamugmar, af al pi she'ein mevi'in es hamugmar ela le'achar haseudah" - Beyond that, it is fitting to honor the one who recited the berachah on the wine with the berachah on the spices as well. It was customary to bring spices or incense at the conclusion of the meal, and one person recites the berachah and fulfills the obligation of the others. The practice is that the person who recited the berachah on the wine that came after the meal is also the one who recites the berachah on the mugmar. And even though the mugmar was brought only after Bircas Hamazon, so that in practice it is no longer connected to the meal itself, nevertheless that same person who recited the berachah on the wine at the end of the meal is the one who recites the berachah on the mugmar and thereby fulfills the obligation of the others.
In summary: In this Mishnah we learned four situations: sitting down to eat without reclining, where there is no establishment of a meal, and each one recites the berachah for himself; reclining, where there is an established meal, and one recites the berachah for them all; wine brought during the meal, where each one recites the berachah for himself, because "ein beis hablia panui," whether because their attention is not free for the berachah or because a person cannot answer amen; and wine brought after the meal, where one recites the berachah for them all, and he is also the one who recites the berachah on the mugmar, even though the mugmar is brought after Bircas Hamazon.