Gemara

(Mishnah - Beis Shamai): One may give Reshus (rights to go in one's property, to others in the Chatzer) [only] before Shabbos;

Beis Hillel say, one may give Reshus [even] on Shabbos.

Question (Ula): What is Beis Hillel's reason? (This is like acquisition on Shabbos!)

Answer (Abaye): Beis Shamai consider Bitul to be transfer of Reshus, which is forbidden on Shabbos. Beis Hillel consider Bitul to be withdrawal from Reshus. This is permitted on Shabbos.

Kesuvos 7a: A case occurred in which R. Ami permitted Bi'ah Rishonah on Shabbos.

Question (Rabanan): A Kesuvah was not written!

Answer (R. Ami): She should seize Metaltelim (movable objects, for a security until he writes a Kesuvah).

Gitin 77b: A Shechiv Mera wrote a Get to his wife shortly before Shabbos. He was unable to give it before Shabbos. He did not expect to survive until after Shabbos.

Rava: He should give to her, for a gift, the place where the Get is resting. She should close the door there [on Shabbos] to acquire it through Chazakah.

Rishonim

Rif (Beitzah 20b): We do not make Hekdesh on Shabbos. This is a decree due to business. We do not separate Terumah and Ma'aser, even to give to a Kohen the same day. This is if the Peros were Tevel from yesterday. If they became Tevel now, e.g. he made a dough on Yom Tov, we separate Chalah and give it to a Kohen. The Yerushalmi says that anyone who made a Kinyan on Shabbos, and all the more so on Yom Tov, whether they were Shogeg, Mezid or deceived, his action takes effect. We learn that any Kinyan of land or Metaltelim lasts.

Rambam (Hilchos Mechirah 30:7): If one sold or gave [a gift] on Shabbos, and all the more so on Yom Tov, even though we lash him, his action takes effect. Whoever acquired from him, the Kinyan lasts, and they write it after Shabbos.

Ran (Shabbos 64a DH Poskin): Why may we pledge Tzedakah on Shabbos? One may not make Hekdesh (Beitzah 36b)! R. Chananel says that the Isur is to be Makdish a known Kli, for it looks like buying and selling, but one may obligate himself to Shamayim through his words. I am still bothered, for one may not be Ma'arich (pledge an amount to Hekdesh based on a person's age and gender). There is no known Kli, yet it is forbidden!

Answer (Beis Yosef OC 306 DH v'Al): Erchin is like buying and selling. It is as if he acquires the person, after pledging his value to Hekdesh. The Kolbo says that we forbid only Hekdesh for the Mizbe'ach or Bedek ha'Bayis, for then it leaves his Reshus and enters Hekdesh's Reshus. A pledge for 'Hekdesh' for a Sefer Torah, crowns, oil [for the Beis ha'Keneses]... is permitted, for nothing was designated to leave his Reshus. It is unlike buying and selling. This is like R. Chananel.

Ran (Kesuvos 2a DH Atfesuha): Why is it permitted to give a security of Metaltelim [for the Kesuvah] on Shabbos? Kinyan is forbidden on Shabbos, like it says in Beitzah 17a! It was permitted for a Mitzvah, like it says in Gitin (77b). The Yerushalmi forbids Nisu'in with a widow on Shabbos, due to Kinyan, even though it is a Mitzvah. This is because it is very publicized. Alternatively, she seized the Metaltelim before Shabbos. There was no time to write a Kesuvah before Shabbos.

Ritva (Kesuvos 7a DH Amar): Some explain that she had to seize Metaltelim before Shabbos, for one may not acquire on Shabbos, even for a Mitzvah, unless it is pressed circumstances. We also permit for a Shechiv Mera (a sick person who fears lest he die), lest he go crazy [due to panic that he cannot bequeath the way he wants - Bava Basra 156b], and one who was about to die and wanted to divorce (Gitin 77b). This is correct. However, here, we need not say so. Here it is not a proper security. It is merely so she will be assured [that if she will be widowed or divorced, she will receive a Kesuvah]. It is like borrowing wine and oil, and leaving his Talis.

Rivash (156): One may not do Pidyon ha'Ben on Shabbos. One may not separate Terumos and Ma'aseros on Shabbos only because it resembles Tikun. There one merely needs to separate, but not Hakna'ah and giving it to the Kohen immediately. One must be Makneh the money to redeem his son. Surely, this is like buying and selling! One may send to a Kohen on Yom Tov Terumah separated beforehand. There, no Kinyan occurs. It already belonged to Kohanim. The Yisrael had only the right to choose to which Kohen to give it. In Pidyon ha'Ben, the separation is nothing. One must be Makneh to the Kohen on Shabbos; this is no less Asur than paying a debt. It is forbidden on Yom Tov, and all the more so on Shabbos. Just like we decree not to lend, lest he write, we decree not to pay. Also, one cannot redeem with regular coins, for they are Muktzeh. If he gives an item that one may move on Yom Tov in place of five Sela'im, this is absolute business, aside from the Pidyon itself. He was obligated to pay five Sela'im, and gives the item in place of it. Also, he must explicitly say "to redeem my son." Also, if the item is not worth five, he must say "for five Sela'im for my son's Pidyon", so the Kohen will accept it in place of five Sela'im, e.g. if the Kohen is distinguished and often he would pay five for it, e.g. like Rav Kahana (Kidushin 8a).

Poskim

Shulchan Aruch (OC 306:6): Cheftzei Shamayim are permitted, e.g. to pledge Tzedakah... make Shiduchim for children, or teach a trade to one's son. One may speak with the other side, but one may not hire or mention an amount of money.

Magen Avraham (11): The Kolbo holds that our 'Hekdesh' is Chulin (CM 95:1), and all Yisrael have a share in it. Therefore, it did not leave his Reshus, for he has a share in it. This is unlike the Beis Yosef.

Kaf ha'Chayim (47): When they give a gold or silver Kli for a gift to a Rav who expounds, he should intend not to acquire it until Motza'ei Shabbos.

Kaf ha'Chayim (48): The Kesav Sofer (OC 59) says that once, someone forgot to sell a cow [about to gave birth for the first time] to a Nochri before Shabbos. One may give it on Shabbos to avoid Kedushas Bechor.

Kaf ha'Chayim (50): Chalipin should not be done on Shabbos to formalize a Shiduch. They should rely on a handshake.

Rema: Some say that where the custom is to make a Mi she'Berach for one who gets an Aliyah, and he pledges to Tzedakah or the Shali'ach Tzibur, one may not pledge on Shabbos. The custom is to be lenient, for one may pledge Tzedakah.

Taz (2): According to the Kolbo, if one designated a Sefer Torah, he may not bring it to the Beis ha'Keneses on Shabbos, for it leaves his Reshus when he makes it for Tzedakah! The custom is to do so. I say that he was already Makdish it before Shabbos. He merely publicizes this on Shabbos. One may not first resolve to be Makdish [for Tzedakah] on Shabbos.

Yam Shel Shlomo (Beitzah 5:8): Auctioning off Mitzvos looks like business. We should forbid, unless we say that business does not apply to Mitzvos, only with items acquired. This is a poor defense of the custom. Surely one may not buy seats in the Beis ha'Keneses, or Esrogim after the Mitzvah finished. It is proper to do like Chasidei Astrich, and give whatever he bid, even if he did not receive the Mitzvah. Then, it is like pledging for a Mitzvah, and unlike business.

Magen Avraham (15): What is the Heter to pledge money for the Shali'ach Tzibur if he is not poor? This is not Tzedakah! Since they give in order that he will pray, it is considered a Mitzvah, just like pledging for building a Beis ha'Keneses. Shiltei ha'Giborim (Avodah Zarah 4a:1) questioned buying Mitzvos. In Bava Kama 32b:3, he wrote that one can sell the Mitzvah he bought to someone else. Buying and selling is forbidden verbally or through Mesirah (handing over an item). This is a decree, lest one write (Rambam 23:12,13).

Magen Avraham (15): The Beis Yosef (527, citing the Mordechai Beitzah 676) forbids gifts on Shabbos and Yom Tov, unless needed for a Mitzvah. Surely it is permitted for the needs of Shabbos (323:7, 516:1). Eruvin 71a connotes like this. It forbids to be Makneh Reshus, even without Chalipin. (See CM 254:1). Gitin 77b connotes like this, that even Kinyan Chazakah is forbidden [if not for a Mitzvah]. See the Rosh (Gitin 8:2). The Ritva (Kesuvos 7a) connotes that one may not even give a security for Chulin. Yalkut Shimoni (Beha'aloscha 720 DH v'Ya'asu (2)) connotes like this. It lists giving a security and buying [Korban Pesach] among matters that override Shabbos. This implies that it is forbidden for the sake of Chulin. Also, Hekdesh is like a gift, and it is forbidden. The Rif and Rambam connote like this. See what I wrote (307:14). If so, what is the Heter for our custom to give gifts of Kelim to a Chasan who expounds on Shabbos? Also, some obligate themselves to give a certain sum. This is forbidden. We permit only to Hekdesh, like I brought above (11) from the Ran! If not, why did we need to teach that one may pledge to Tzedakah? This requires investigation. We can say that here he does not obligate himself through his words, unlike Hekdesh.

Kaf ha'Chayim (41): People rely on the Magen Avraham to give a Sefer Torah even if they were not Makdish it before Shabbos. People pledge to the Shali'ach Tzibur, for this is mere speech.

Mishnah Berurah (33): Where the custom is to permit auctioning Mitzvos on Shabbos, we do not protest. One may not buy an Esrog from a seller on Yom Tov. One may give a gift needed for Shabbos or Yom Tov (323:7), or for a Mitzvah. It is improper to give a Kli to a Chasan on Shabbos. One may obligate himself to give money, for he can retract.

Kaf ha'Chayim (42): The custom is to auction Mitzvos, and one who did not receive it does not pay anything.