Gemara

32a (Mishnah): If Reuven was running in a Reshus ha'Rabim and Shimon was walking, or both were running, and Heziku (they damaged) each other, they are exempt.

Our Mishnah is unlike Isi ben Yehudah.

(Beraisa - Isi ben Yehudah): The one running is liable, for this is abnormal.

Isi admits that Bein ha'Shemashos (twilight) of Erev Shabbos he is exempt, for he is allowed to run.

Question: R. Yochanan said that the Halachah follows Isi, and he also said that the Halachah follows a Stam (anonymous) Mishnah!

Answer: Our Mishnah is like Isi. It discusses Bein ha'Shemashos of Erev Shabbos.

Support (Reisha): If both were running, they are exempt.

Question: Why is this needed? Even if one runs and the other walks, he is exempt. All the more so, if both are running they are exempt!

Answer: Rather, the Mishnah teaches that if Reuven was running and Shimon was walking, Reuven is exempt. This refers to Erev Shabbos, Bein ha'Shemashos. At any other time, Reuven is liable;

If both were running, even during the week they are exempt.

Question: Why may one run during Bein ha'Shemashos of Erev Shabbos?

Answer: This is like R. Chanina. Bein ha'Shemashos of Erev Shabbos, he would say 'come, let us go out to greet (Shabbos) the bride, the queen.'

R. Yanai would cloak himself, stand and say 'come bride, come bride.'

48b (Rava or Rav Papa): If two people were both acting in a permitted way or both in a forbidden way and Heziku each other, they are liable. If Huzku (they got hurt) through each other, they are exempt.

(Inference): This is because they were both the same. If only one had permission, he is exempt and the other is liable.

Rishonim

The Rif (14b) brings the Mishnah.

Nimukei Yosef DH she'Hu): One has permission to run to buy needs of Shabbos. Whether they were heading towards each other or going one after the other, he is exempt. When both were running, we exempt on Shabbos or during the week. We can distinguish which way they were going, like we do regarding a collision between one carrying a beam and one carrying a jug (31b). If the one in front stopped, he is responsible. If the one in back went faster, he is responsible. The Ramah says that we exempt on Erev Shabbos when we may assume that he was running for needs of Shabbos. Stam, we say so. We follow the majority. Even if his hands are empty, he must say 'did you tithe? Did you make an Eruv?' Perhaps he needs to wash his hands, feet and face, or change his clothes. R. Yanai would dance out and return and say 'come bride, come bride'. (This is unlike our text.) Even this is considered a Mitzvah, for it is to honor Shabbos.

Rambam (Hilchos Chovel u'Mazik 1:16): If two people acted with permission, or neither had permission, and they damaged each other, they are exempt.

Magid Mishneh (and Beis Yosef CM 378 DH u'Mah she'Chosav Hayu): Rashi explains that Heziku means that they overtly damaged each other, even without intent, they are liable. Regarding Nezikim we do not distinguish between with and without intent. If Huzku, i.e. they were damaged by one another, they are exempt. A Mishnah (32a) exempts two who Heziku each other. It really refers to a case of Huzku. If they Heziku, they would pay. The Rashba says the same.

Ramah (cited in the Tur): If both were running, even if they damaged each other, they are exempt. We say that one is liable only if he did an act through which the other was damaged, and the other did nothing. If both were running, they both did an act, so it is as if they were damaged by each other, and they are exempt.

Beis Yosef (DH u'Mah she'Chosav Rabeinu b'Shem): This resolves the Mishnah and Beraisa. We need not give Rashi's difficult answer that the Tana said 'Heziku', but he means 'Huzku.'

Rambam (6:9): Reuven was running in a Reshus ha'Rabim and Shimon was walking, and one was damaged through the other without intent , Reuven is liable, for he deviated. If it was Erev Shabbos Bein ha'Shemashos, he is exempt, for he is allowed to run, lest Shabbos enter and he is not free. If both were running and they were damaged through each other, they are exempt, even on other days.

Prishah (CM 378:8): This connotes that even if he was running to finish his affairs before Shabbos, he is exempt. If so, everything is included! Rather, he runs to finish the needs of Shabbos, like the Rema says.

Rosh (3:11): Isi obligates one who was running, unless it was Erev Shabbos Bein ha'Shemashos, for he was allowed to run to toil to honor Shabbos. If both were running and damaged each other without intent, they are exempt. This is the Halachah.

Hagahos Ashri: This implies that one who ran is exempt not only Bein ha'Shemashos, rather, from when people begin to bake, cook and roast for Shabbos, i.e. after midday.

Poskim

Shulchan Aruch (CM 378:7): If both of them had permission or neither had permission and they were damaged through each other's body or property, if they did not know that the other is there, they are exempt. If they saw each other, even though they did not intend, they are liable.

Gra (20): We distinguish whether or not they saw each other only in the damage's Reshus! He should distinguish like this in Sa'if 6! Also, here he does not say that one is liable only for overt damage! Really, the distinction between knowing and not knowing belongs in Sa'if 6, after exempting for damage in the damager's Reshus. Here it should say that they are liable only for overt damage, like the Gemara says. This explains the continuation of the Shulchan Aruch 'therefore...'

Shulchan Aruch (ibid.): Therefore, if both were running in Reshus ha'Rabim, or both were walking and they were damaged through each other, they are exempt. If'/ they damaged each other, they are liable.

SMA (10): When both were running, they are exempt only if they did not see each other.

Shulchan Aruch (8): If Reuven was running and Shimon was walking, and Shimon was damaged through Reuven, Reuven is liable, for he had no permission (to run). This refers to a weekday. If it was Erev Shabbos Bein ha'Shemashos, he is exempt, for he had permission.

Beis Yosef (DH v'Chosav ha'Mordechai): The Mordechai exempts only for this Mitzvah Bein ha'Shemashos, for there is no time. If he was running to another Mitzvah, e.g. to the Beis ha'Keneses or Beis Medrash, which can be done later, and he damaged, he is liable.

Rema: Stam, we assume that he was running for the needs of Shabbos. If we know that he was running for his other desires, he is liable like on a weekday.