"The Interlopers" by Saki is set in the forest of the Carpathians on a stormy winter night; the two main characters are Ulrich von Gradwitz and Georg Znaeym and they are feuding. This is not a small-time feud, however, and the stakes prove to be significant.
Georg and Ulrich are the youngest participants in a three-generation feud, and they do more than just despise one another. The feud is over a "worthless strip of forest," but neither side is about to concede ownership to the other.
The feud might, perhaps, have died down or been compromised if the personal ill-will of the two men had not stood in the way; as boys they had thirsted for one another's blood, as men each prayed that misfortune might fall on the other....
Tonight, both men have come to the forest with a hunting party, and they have only one thing in mind: each intends to hunt and kill the other.
This is the conflict, and the men, without their hunting parties, do come face to face. It is a weighty thing to kill another human being, however, and in their moment of hesitation, nature takes matters into her own hands and drops a large tree on them. The two men are pinned beneath the trunk, and there is no way for them to escape on thier own. They are forced to wait until one of the hunting parties comes to rescue them, and the ugliness of the feud continues even in these conditions.
Each man levels threats against the other, assuring his rival that if his men come first, he will be sure to kill the other. The vitriol is palpable, and there does not seem to be any way to end the enmity between them. Soon the men are silent, however, and Ulrich begins to think.
An idea was slowly forming and growing in his brain, an idea that gained strength every time that he looked across at the man who was fighting so grimly against pain and exhaustion. In the pain and languor that Ulrich himself was feeling the old fierce hatred seemed to be dying down.
Ulrich finally offers his former enemy a drink of wine from his flask and suggests that he does not intend to continue the feud; Georg has to think about this offer for a very long time but eventually accepts it. The men even laugh thinking about the reaction in the town to their newly forged friendship.
You ask how the two men are reconciled, and the answer is fairly simple: when forced to really stop and think about the feud and the enemy, the men just decide that they will no longer perpetuate the feud. Georg and Ulrich are the only two who could have made this decision, and they could only have made it under some kind of desperate circumstances.
The irony of the story, of course, is what happens to them as soon as they decide to end their feud and become friends.