Gemara

(Mishnah): Chachamim permitted four vows: vows of urging...

The following are vows of urging. Levi was selling an item, and he vowed not to (benefit from the money he receives, or from a certain food, if he will) sell it for less than four. David vowed not to pay more than two. Both of them want the price to be three.

(Gemara - R. Aba bar Mamal, to R. Ami): You said that R. Yehudah Nesi'ah said that our Mishnah is like R. Yehudah, citing R. Tarfon.

(Mishnah - R. Tarfon): (If six men saw a man walking towards them, and each of them accepted Nezirus contingent on the identity of the man, or on whether or not their colleagues became Nezirim,) none of them is a Nazir, for Nezirus (like Nedarim) requires Hafla'ah (a definite acceptance).

Rejection (Rava): Our Mishnah is even like Chachamim. It does not say that they (later) agreed upon three, rather, they both want (at the time they vowed) three.

Question (Ravina): If the seller vowed not to accept less than 'more than four', or the buyer vowed not to pay more than 'less than two', are these proper vows, or are they vows of urging (that are permitted)?

Answer (Rav Ashi - Mishnah): If Reuven was refusing to eat by Shimon, and Reuven vowed not to enter Shimon's house, and not to drink even a drop of cold drink (from Shimon), he may enter the house and drink cold drink. He intended to forbid only eating and drinking.

Question: He said that even a drop of cold drink is forbidden!

Answer: Rather, (in such cases) people do not mean what they say. Also the buyer and seller do not mean what they say!

Objection (Ravina): That case is different!

Tzadikim make small offers and do much more. (If Reuven would agree to drink a drop, Shimon would serve him a full meal.)

Here, we have a doubt. Perhaps each really intends to compromise on the price, and the vows are of urging;

Or, perhaps each is adamant not to budge, and the vows are real vows!

This question is unresolved.

Rishonim

The Rif brings Rav Ashi's answer and Ravina's rejection.

Beis Yosef (YD 232 DH u'Mah she'Chosav Rabeinu v'Davka): The Ran says that Ma'amid means that he intended for a vow. The Tur explains it to mean that he did not compromise.

Nimukei Yosef (6b DH Konam): I prefer the text of the Yerushalmi that says 'if he was Ma'amid to one of them, but not to the other, since one (the latter) needs no Heter, also the other.' I.e. if David and Moshe wanted to buy from Levi, and he vowed not to sell to either for less than a certain amount, and intended for a real vow regarding David, but only to urge Moshe, since it is Batel regarding Moshe, it is Batel even regarding David.

Rambam (Hilchos Nedarim 4:3): Vows of urging are permitted. If Levi was selling an item, and he vowed to sell it only for four, and David vowed to pay only two, and they agreed on three, they are exempt. The same applies to every similar case. This is because each did not resolve, and did not vow. He said so only to urge the other.

Or Some'ach: The Rambam says 'each did not resolve' to teach the Yerushalmi's law, that he may even sell it for two. Even if he intended not to sell for less than three, since he did not say so, and he did not mean what he said, nothing took effect.

Kesef Mishneh: Why did the Rambam omit Ravina's case? Perhaps since he exempts only when they demanded four and two, we understand that if they were further apart, they are forbidden. Still, he should have said so explicitly.

Rosh (3:1): Ravina's question was not settled. We are stringent. The Yerushalmi says that if they were Ma'amid, vows of urging need a Heter Chacham. If only one of them was Ma'amid, since the other one is permitted, also the Ma'amid is permitted. The Re'em says that if one did not intend just to urge, rather, for a real Neder, it is a Neder, for his mouth and heart concurred.

Poskim

Shulchan Aruch (YD 232:2): The following are vows of urging. Levi was selling an item, and he vowed not to benefit from a loaf if he will sell it for less than four. David vowed not to pay more than two. They agreed on three (Rema - or a little more or less). Neither is forbidden, for it is the way of merchants to vow or swear to urge the other party. He did not intend for a vow.

Beis Yosef (DH u'Mah she'Chosav Nidrei): Because it is normal, this is not Devarim sheb'Lev (unspoken intents, which are invalid).

Taz (1): The Rema cites the Ran. Why must it be only a little more or less than three? The Ran (21a DH Garsinan, cited in the Rema below) says that some forbid selling for two or buying for four, for they explicitly forbade this. All permit to sell or buy for (any amount) more than two or less than four! It seems that the Rema explains that we forbid even close to two or four. The final price must be in the middle, close to each of their demands.

Rema: Some say that even though he intended to urge, the seller cannot sell it for two, and the buyer cannot pay four. Some are lenient.

Taz (4): People conduct like the lenient opinion.

Shulchan Aruch (ibid.): This is only if they were not Ma'amid and agreed upon three. If each stuck to his price and the item was not sold, surely each intended for a proper Neder, and it takes effect. If only one of them was Ma'amid, since the other man does not need a Heter, also the Ma'amid does not. This refers to Stam. If they say that they intended for a real Neder, it is a Neder.

Shach (4): Even if it was a vow, he may sell to someone else for two. He can say 'to him, I consent to sell cheaply.'

R. Akiva Eiger (1): The Ran (23a DH Ein) says that (perhaps) even if they intended for Nedarim, we suggest 'had you known that he would not agree to your price, would you have vowed?' to permit it.

Shulchan Aruch (ibid.): If the seller vowed not to accept less than more than four, or the buyer vowed not to pay more than less than two, this is a proper vow, for it is not normal to urge when they are so far apart. They intended for a proper vow.

Taz (5): When the Gemara says 'v'Halah', it means 'or this one' (the seller demanded more than four, or the buyer insisted that he will pay less than two). The Ran says that more (or less) than four or (two) Dinarim means a Perutah more (or less), for we see that they are exact. Alternatively, it means a Dinar more (or less), for they are far apart. The Rosh (21a DH Omar) connotes like the latter version. I do not understand why it matters if they differ by more than two Dinarim. The Tur and Shulchan Aruch are like the former version. We cannot say that for a little more or less they are called 'far apart.'

Shach (5): According to the former version, even if they differ by just over a Dinar, if one was precise to demand a bit more than four (or a bit less than three), it is a vow.

Rema: If David and Moshe wanted to buy from Levi, and Levi vowed, and says that he intended for a real vow regarding David, but only to urge Moshe, since it is Batel regarding Moshe, it is Batel even regarding David.