Gemara

(Mishnah #1): If Reuven stole a Perutah from Shimon and swore that he did not, Reuven must return it, even if Shimon lives overseas. It suffices to give it to a Shali'ach of Beis Din.

103b - Inference: One must travel to return theft only if he swore falsely about it.

Question (Mishnah #2 - R. Tarfon): If Reuven is unsure from which one of five people he stole, and each of them says 'you stole from me', he may leave the theft in front of them and go away;

R. Akiva says, to correct his sin he must pay the value of the theft to each.

Mishnah #1 is unlike R. Tarfon, who allows leaving the theft in front of them even if he swore. It is unlike R. Akiva, who obligates paying every one of them even if he did not swear!

Answer #1: Really, it is like R. Akiva. He obligates paying every one only if he swore falsely, for it says "la'Asher Hu Lo Yitnenu b'Yom Ashmaso." R. Tarfon holds that even though he swore, Chachamim made an enactment for the thief (to leave what he owes with Beis Din). R. Akiva holds that we enacted only for one who knows from whom he stole, for then the victim can get his money back.

Objection #1 (Rav Huna bar Yehudah - Beraisa - R. Shimon ben Elazar): All agree that if one does not know from which person he bought, he may leave what he owes in front of them. R. Akiva and R. Tarfon argue about one who does not know from which one person he stole, and all of them claim from him. R. Tarfon says that it suffices to leave the theft in front of them. R. Akiva says, to correct his sin he must pay each of them the value of the theft.

If he swore, the same should apply whether he bought or stole!

Objection #2 (Rava - Beraisa): A case occurred in which a Chasid was unsure from which of two men he bought. R. Tarfon told him that it suffices to leave the money in front of them. R. Akiva told him that to clear himself he must pay each.

Since he was a Chasid, surely he did not swear falsely!

Answer #2: Really, Mishnah #1 is like R. Tarfon. He agrees that one who swore must pay each one, due to "la'Asher Hu Lo Yitnenu b'Yom Ashmaso."

Question: The verse discusses one who (brings a Korban, which is only if he) admitted his sin. If so, R. Tarfon obligates him even if he did not swear!

(Beraisa): R. Tarfon agrees that if one tells two people who he is not sure from which of them he stole that he must pay both, for he admitted.

Answer (Rava): Mishnah #1 is different. Since he knows from whom stole and admitted to him, it is as if Shimon said 'the theft is like a deposit with you.' Reuven must travel to return it only if he swore (and must bring an Asham).

Bava Metzia 37a - Contradiction (Mishnah #3): If Reuven told two people 'I do not know from which of you I stole', he pays both, for he admitted by himself.

Suggestion: Perhaps Mishnah #3 is not like R. Tarfon (rather, it is R. Akiva)!

Rejection (Beraisa): R. Tarfon admits that if one tells two people 'I do not know from which of you I stole' that he pays both.

Answer: In Mishnah #1, they claim from him. Letter of the law, he may leave the theft in front of them. Here, he wants to be Yotzei Yedei Shamayim.

Support (Mishnah #3): He pays both because he admitted by himself.

Rishonim

Rif (Bava Metzia 20b): We infer from 'he pays both because he admitted by himself' that he wants to be Yotzei Yedei Shamayim, but letter of the law he needs to pay only once. When they claim from him, each swears and collects, like R. Akiva. The Halachah follows him against R. Tarfon, his colleague. Even though we do not force one to pay due to Safek, rather, we leave money in its Chazakah, here Chachamim fined him because he transgressed an Isur Torah.

Rebuttal (Ba'al ha'Ma'or Bava Kama 36b): Some texts say 'Ela (rather), Rava said...' I.e. our Mishnah is even like R. Akiva. This is wrong. If so, why did it say that he swore? Even if he didn't swear, if witnesses came he must travel to Madai. Since he denied stealing, surely Shimon does not consent that the theft be a deposit with him! Rather, the Mishnah is like R. Tarfon. Rav Hai Gaon rules like R. Tarfon.

Defense (Milchamos Hash-m): We thought that it does not matter whether or not he knows from whom he stole. Rava teaches that all distinguish. We fine only when the victim will not get back his money, according to R. Tarfon if the thief swore, or according to R. Akiva, even if he did not swear. Even if the text doesnt say Ela, perhaps the Gemara did not retract, e.g. Pesachim 73b...

Rebuttal (Shach CM 365:2): In all the Ramban's examples, the Gemara says Ela! Tosfos (104a DH Omar) says that if the text does not say Ela, the Mishnah is only like R. Tarfon. Rav Hai Gaon and Bahag hold like the Ba'al ha'Ma'or. Even if the text says Ela, perhaps we retract only from saying that R. Tarfon discusses only if he did not swear. Even if the Mishnah is also like R. Akiva, perhaps he was R. Tarfon's Talmid (Kesuvos 84b), and the Halachah follows R. Tarfon. Also, perhaps the Halachah does not follow R. Akiva against his colleague regarding a fine. This is the intent of the Nimukei Yosef (below). Even though most rule like R. Akiva, the thief can say that he holds like the Ba'al ha'Ma'or, Rav Hai Gaon, Bahag and Ra'avad.

Nimukei Yosef (21a DH Gemara): The Halachah follows Rav Nachman (Bava Kama 118a), who exempts one who is unsure whether he owes, unless he transgressed. Therefore, R. Akiva's law is like a fine. Nowadays, we do not collect fines. This is why the Ra'avad and Ba'al ha'Ma'or rule like R. Tarfon.

Rambam (Hilchos Gezeilah 4:9): If one does not know from which one of five people he stole, and each says 'you stole from me', even though there are no witnesses of the theft, each swears and receives the theft. This is a fine mid'Rabanan. The Torah does not require him to pay due to Safek.

Rosh (Bava Metzia 3:8): The Stam Gemara infers that our Mishnah obligates only one who wants to be Yotzei Yedei Shamayim, like R. Tarfon. Even so, the Halachah follows R. Akiva against his colleague. Each claimant swears and collects. Our Mishnah is also like R. Akiva, for he agrees that when there are no claims against the thief, he pays each only if he wants to be Yotzei Yedei Shamayim. If one does not know whether or not he stole, he is exempt even b'Yedei Shamayim, like it says in Bava Kama 118a.

Poskim

Shulchan Aruch (CM 365:1): If one does not know from which one of five people he stole, and each says 'you stole from me', even though there are no witnesses of the theft, each swears and receives the theft.

Beis Yosef (DH u'Mah she'Chosav Kol): The rule is, anyone who collects due to his words must swear. Alternatively, since letter of the law he is exempt, and it is a fine that he must pay each, it is improper to fine him without an oath.

Rebuttal (Gra): We need not find new reasons for the oath. Shevu'os 47b says that when we are unsure which of two lenders a borrower owes, this is like the Mishnah (45a; both swear and collect).

SMA (2): Each swears holding a Chefetz (Sefer Torah or Tefilin...). Even though the thief does not have a definite claim against them, since he knows that he stole only from one and both come to collect, Chachamim imposed an oath on them, like one who swears and collects.