Gemara

(Mishnah): If a widow's Kesuvah was 200 Dinarim and she sold property of the orphans that was worth 100 for 200, or property worth 200 for 100, in either case she received her full Kesuvah.

Question: When she sells land worth 200 for 100, the orphans tell her that she lost. When she sells land worth 100 for 200, why can't she say that she profited?

Answer (Rav Nachman): In our Mishnah, Rebbi taught us that the owner of the property receives the profits.

(Beraisa - R. Yehudah): If a Shali'ach bought something, and the seller gave one extra, the Shali'ach keeps it;

R. Yosi says, he shares it with the Meshale'ach (the one who sent him).

Contradiction (Beraisa - R. Yosi): The Meshale'ach keeps the extra one.

Answer (Rami bar Chama): If the sold item has a fixed price, they share the extra one. If the price varies, the Meshale'ach keeps it.

(Rav Papa): This is the Halachah.

Rishonim

Rif and Rosh (11:15): Produce is something with a fixed price. One receives a known number, weight or volume (for a Shekel). If the seller gave more, the Shali'ach and Meshal'ach share it. Since the Shali'ach benefited through the Meshale'ach, they share the profit.

Ran (DH Gemara): If the price varies, such as a garment or vegetables sold by estimation, sometimes a seller pardons and sells cheaply, and sometimes he sells precisely. This is not a gift, so the Meshale'ach keeps it all. According to the Rif, even if the seller explicitly says that it is a gift to the Shali'ach, since the benefit came through the Meshale'ach, they share it.

Rosh: A case occurred in which a Nochri gave extra money to a Shali'ach; they could not find the Nochri to return to him. R. Tam ruled that the Shali'ach and the Meshale'ach share the profit, for money is like something with a fixed price, and the Shali'ach profited through the Meshale'ach's money. Rashi said that we are unsure whether the gift was intended for the Shali'ach or for the Meshale'ach.

Rebuttal (R. Yo'el, cited in Hagahos Ashri): Our Mishnah discusses an error! The Yerushalmi asks that the extra must be returned, for it is a Mekach Ta'os! It answers that the bought item rose in price. Rather, when there is a fixed price, the Mazal of the Shali'ach and Meshale'ach caused the error. Therefore they share it. When there is no fixed price, the error was due to the (property of the) Meshale'ach.

Rosh (ibid.): Rashi's reason does not apply to a mistake. Nevertheless, also this reason is primary, and he is Muchzak, therefore he has the upper hand, and they split it. This is even if the Shali'ach was paid. The owner is not particular if the Shali'ach picks up a (Hefker) Aveidah while working. Surely, if the Shali'ach found a wallet, he would keep it! R. Tam retracted, and said that any mistake goes to the Meshale'ach, like the Mishnah. This is unlike a seller who gave extra; that was not a mistake. The Ri says that the Shali'ach gets it all. If he stole or swindled, the Meshale'ach has nothing to do with this. This is unlike other errors, in which the seller thought that his merchandise was worth more than the money, and he sent it all to the Meshale'ach. Here, the Nochri knows the amount he owed. His error is by itself, as if the Shali'ach stole it. The Shali'ach could have told the Nochri about the mistake and returned it! It would be astounding to say that he is not allowed to do so. This opinion is primary.

Beis Yosef (CM 183 DH v'Chosvu ha'Tosfos): The Mordechai supports this. If the Nochri realized his error, he would claim from the Shali'ach, who took the money! R. Yerucham ruled like R. Tam in one place, and elsewhere like the Ri. Ba'al ha'Itur rules like R. Tam before he retracted (they share the extra).

Darchei Moshe ha'Aruch (183:8): The (Rashba, Teshuvah 60 attributed to the) Ramban says that Rashi's opinion is primary. If the seller explicitly says that it is a gift to the Shali'ach, the Shali'ach keeps it all. If a community appointed Reuven to be a Shali'ach to collect a tax and pay a Nochri, and the Nochri gave a gift to Reuven, he can claim that the gift was not due to the community, rather, it was because he benefited the Nochri. Even the Rif would agree to this.

Hagahos Ashri: The Rashbam wrote that if David told Levi 'sell this for five', and he did not say 'the excess will be yours', and Levi sold it for six, David gets all six, for the price is not fixed. If the Nochri erred by himself and they cannot find him to return to him, the Shali'ach keeps the extra one himself.

Rambam (Hilchos Sheluchim 1:5): If there was a fixed, known price, and they gave to the Shali'ach more than the usual number, weight or volume, he and the Meshale'ach share the excess. If the price varies, the Meshale'ach keeps it all.

Kesef Mishneh: Rashi said that we are unsure whether the gift was intended for the Shali'ach or for the Meshale'ach. The Rif says that since the Shali'ach benefited through the Meshale'ach, they share the profit. It seems that this applies even if he explicitly said that he gives a gift to the Shali'ach. It seems that the Rambam agrees. The same applies to a Nochri who erred and gave too much. Tosfos says that if a Shali'ach was given 200 to pay to a Nochri and he tricked the Nochri and paid only 100, the other 100 belonged to the Meshale'ach the entire time.

Poskim

Shulchan Aruch (CM 183:6): If there was a fixed, known price, and they gave to the Shali'ach more than the usual number, weight or volume, the Shali'ach and Meshale'ach share the excess.

SMA (18): The Rif holds that letter of the law, it all belongs to the Shali'ach. Chachamim enacted that the Meshale'ach gets half because it came through his money.

Shulchan Aruch (ibid.): If the price varies, the Meshale'ach keeps it all.

Rema: If the seller explicitly said that he gives a gift to the Shali'ach, the Shali'ach keeps it all.

SMA (18): Even though the Rema rules like Rashi, a judge may rely on the Rif and Rosh when he sees fit.

Question (Shach 12): Why does the Rema omit the opinions that disagree, i.e. the Rif, Rosh, Ba'al ha'Itur, and Ran? The Yerushalmi supports them!

Shulchan Aruch (7): If a Shali'ach was sent to collect money from a Nochri, and the Nochri mistakenly gave extra, the Shali'ach keeps it all.

Question (SMA 21): Why did the Shulchan Aruch and Rema omit the law of a Nochri who erred about a sale? R. Tam holds that the Meshale'ach gets it all, and the Ri and Rosh say that they divide it!

Rema: This is only if the Shali'ach knew about the error before the money came to the Meshale'ach. If not, the Meshale'ach keeps it all. If Moshe was dealing with a Nochri and Yakov helped him and tricked the Nochri about the number, weight or volume, they split the profit, whether Yakov was paid or helped for free.

Shach (14): The Shali'ach does not acquire without knowledge. This applies also in Sa'if 6 regarding something with a fixed price.

Source (Gra 23): One who bought a Chatzer does not acquire a Metzi'ah in the wall, because this is unusual and he did not intend for it (Hagahos Ashri Bava Metzi'a 2:9 DH Kosav). Tosfos (Bava Metzi'a 26a DH d'Shasich) says that it is because the Metzi'ah was not destined to be found.

Source (Beis Yosef DH v'Chosav Od): The Mordechai says these laws. In the latter case they share because neither would have profited without the other. I say that perhaps the Rif would agree in this case, for the error is by itself. Had Yakov stolen from the Nochri, Moshe would have no share in it!

Support (for Beis Yosef - Shach 13): The Rosh holds like the Rif, and he says that in this case Yakov keeps everything. The Beis Yosef wrote otherwise in the Kesef Mishneh (that the Rif says that they share it even in this case).