Gemara

(Mishnah #1): If a house fell, and Shimon (who owns the Aliyah) wants to rebuild it, but Reuven (who owns the ground floor) refuses, Shimon may build (the ground floor) and live there until Reuven pays Shimon's expenses.

R. Yehudah says, even in this case, one who lives in another's yard without his Da'as must pay rent. Rather, Shimon builds both stories, and lives in the house until Reuven pays (for the ground floor).

Bava Kama 20a - Question (Rav Chisda): If Reuven lived in Shimon's yard without Shimon's Da'as (knowledge or consent), must he pay rent?

If the yard is not normally rented, and Reuven does not normally rent a place, Reuven didn't benefit, and Shimon didn't lose (surely, Reuven is exempt)! If the yard is normally rented, and Reuven normally rents a place, Reuven benefited and Shimon lost (surely, Reuven must pay)! Rather, he asked about a yard that is not normally rented, and Reuven normally rents a place.

20b - Answer #1 (Rami bar Chama - Mishnah): (If an animal ate food in Reshus ha'Rabim, it is exempt.) If it benefits, it pays the benefit.

Rebuttal (Rava): There, the damager benefits, and the owner of the food loses. Rav Chisda asked about when Reuven benefits and Shimon does not lose!

Rami bar Chama assumes that one who left food in a Reshus ha'Rabim made it Hefker (so also he does not lose).

Answer #2 (Mishnah #1): If Reuven refuses to rebuild, Shimon may build and live there until Reuven pays Shimon's expenses;

R. Yehudah says, even in this case, one who lives in another's yard without his Da'as must pay rent.

Inference: When Shimon benefits from Reuven, and Reuven does not lose, Shimon must pay!

Rejection: There, Reuven loses. Living in a new house blackens the walls.

Answer #3 (Bei R. Ami): Since Reuven caused no loss to Shimon, he is exempt!

Rishonim

Rif (Bava Kama 9a): If the yard is normally rented, Levi must pay, even if he does not normally rent a place, for he makes Yehudah lose.

Rambam (Hilchos Gezeilah 3:9): If Levi lived in Yehudah's yard without Yehudah's Da'as, if the yard is normally rented, even if Levi does not normally rent a place, he must pay, for he made Yehudah lose.

Magid Mishneh: The Gemara did not discuss this case. The Rambam obligates, like the Rif. Tosfos exempts.

Rosh (Bava Kama 2:6): The Ri says that even if a yard is normally rented, if Levi does not normally rent a place, he is exempt. Since he did not benefit, even though he caused a loss, he is exempt. Even if he expelled Yehudah from the house and locked him out, this is only Gerama (causation), and he pays like the time of the theft.

Pilpulei Charifta (30): Perhaps he means that even if he is considered a thief, he pays like the time of the theft, so it suffices to return the house later.

Rosh (ibid.): Similarly, if one accepted to work a field and left it fallow, he is liable only because we expound the text of commoners (written in the document). The Yerushalmi learns from here that one who prevents another from profiting is exempt. The Rif says that if the yard is normally rented, Levi must pay, even if he does not normally rent a place, for he makes Yehudah lose. The Gemara supports this. Bei R. Ami exempts Reuven, for he caused no loss. This implies that if he caused a loss, he is liable, even if he did not benefit. However, I proved that he is exempt for the loss, for it is Gerama. He is liable only because he consumed the other's loss. This is unlike locking one out of his house, or leaving a field fallow, in which he did not benefit from the owner's loss. Here, even though he could have lived elsewhere, he benefited from the owner's loss.

Bach (CM 363:6 DH v'Ha): Why is locking one out of his house different than locking one in a room (so he cannot work), for which one is liable? When one is locked out of his house, the damage does not start immediately, only later when he cannot rent it out.

Rebuttal (Ketzos ha'Choshen 3): Also when one is locked in a room, the damage starts only when he cannot hire himself! Rather, the Torah obligates for five damages to man, including Sheves (temporary inability to work). Only permanent Nezek is paid for damage to an animal or other property.

Hagahos Ashri: Mahari'ach rules like the Ri. Or Zaru'a rules like the Rif. Avi ha'Ezri says that if no one was trying to rent it, he is exempt, even though if the owner were here he would rent it. Since the owner or his Shali'ach is not here, it is like a yard that is not normally rented. Some disagree.

Nimukei Yosef (DH v'Chatzer): Tosfos exempts, like Mevatel Kis Chavero (preventing another from profiting). The Ro'oh says that the Ge'onim and his Rebbi disagree. Mevatel Kis is only Gerama. One who eats another's Peros is liable, even if he did not benefit! However, if he did not live there, he is exempt. The Ramah says that if he lived there he is liable, like all damages in which the damager does not benefit, even according to the opinion that does not obligate for Garmi (kinds of Gerama that are close to overt damage).

Poskim

Shulchan Aruch (363:6): If the yard is normally rented, even if Levi normally does not rent a place, he must pay, for he made Yehudah lose.

Darchei Moshe (2*): The Nimukei Yosef (Bava Kama 8b) says that all Ge'onim hold like the Rif. In Bava Metzia he says that all the Acharonim hold like Tosfos.

Note: In Bava Metzia 71b he says that the Rashba and Ran hold like Tosfos.

Gra (18): The Rif inferred from Bei Rav that Levi is liable whenever Yehudah loses (in the Rosh above). Sa'if 7 brings Tosfos' opinion. Rami bar Chama proved from the Mishnah that even though the victim loses, the damager is liable only if he benefited. Rava agreed that Levi is liable for Yehudah's loss only if Levi benefits. However, Rav Chisda asked about when Levi benefits and Yehudah does not lose!

Rema: If he was not living there, even though he stole it from him, he is exempt from paying rent. Nowadays, Stam houses are normally rented, even if he never rented it.

SMA (17): If Levi lived in it, even without benefit, he is liable for consuming Yehudah's money. If he did not live in or benefit from it, it is only Gerama.

Gra (21): In the Seifa (Bava Metzia 117b), Shimon builds both stories, and may live in the house until Reuven pays the expenses. Even though Reuven loses, Shimon is exempt because he does not gain (he could live in the Aliyah)! How can the Rif argue with this? We must say that the Rif agrees in a case when Reuven loses a tiny amount (blackening of walls). Some obligate only the amount of the loss.

Note: Tosfos (Bava Metzia 117a DH v'Yoshev) explains that Shimon lives in the Aliyah, and Reuven does not lose at all! Or, the Rif could hold that the gain of being settled outweighs the blackening of the walls, even though Reuven did not want to build yet.