The Shulhan Aruch (Orah Haim 200) addresses the case of three people who ate together, and are thus required to recite a Zimun before Birkat Ha’mazon, but two finish eating before the third. If they do not want to wait for the third to finish eating, the Shulhan Aruch writes, then they are entitled to compel the third to stop eating so a Zimun can be recited. After the Zimun, the third may continue eating, and he of course then recites Birkat Ha’mazon. The Shulhan Aruch adds that even if the third does not respond to the Zimun, the two have nevertheless fulfilled their obligation by making the Zimun (though the third, quite obviously, has not fulfilled his obligation).
In the reverse case, however, when only one of the three has finished eating and wishes to recite Birkat Ha’mazon so he can leave, he does not have the right to compel the other two to interrupt their meal to respond to a Zimun. Of course, if they agree to interrupt as a courtesy to their fellow, they certainly may do so, but this is not required.
There are, however, a number of exceptions to this law. The Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939) writes that if the one who wishes to leave is the father or the Rabbi of the other two, then out of respect for their father or Rabbi, they must stop their meal, and may not make the father or Rabbi wait for them to finish. Additionally, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes that if the one who finished eating urgently needs to leave, and risks incurring a financial loss by waiting for the other two, then it is proper for the other two to interrupt their meal for a Zimun. The Mishna Berura adds that if the other two refuse, then the one who needs to leave is allowed to recite Birkat Ha’mazon and leave without a Zimun, as he is not required to incur a financial loss for the sake of a Zimun.
It should be noted that according to the practice of the Sepharadim, those who interrupt their meal for a Zimun need to stop eating only for the Zimun itself, until the leader of the Zimun repeats, "Baruch She’achalnu Mi’shelo U’b’tubo Hayinu." (This is in contrast to the Ashkenazic custom, which requires them wait until the leader of the Zimun completes the first Beracha of Birkat Ha’mazon.) This means that interrupting one’s meal for a Zimun involves just several seconds. Certainly, then, although two people are not required to interrupt their meal for the third who wishes to leave, it would certainly be appropriate for them to do so, given that the inconvenience entailed is hardly significant.
Summary: If three people ate together, and two finish eating before the third, they are entitled to force the third to interrupt his meal so they can conduct a Zimun. In the reverse case, where one person finished before the other two, he cannot force them to interrupt their meal for a Zimun, unless they are his sons or students, or he risks incurring a financial loss by waiting for them. However, given that the inconvenience entailed is minimal, it would certainly be proper as a matter of courtesy for the other two to interrupt their meal for the several seconds required for a Zimun.