For example, a friend invited me to a party at his house. I brought apple juice with me. Suddenly, the police burst in, and it turns out that juice is prohibited in his contractual jurisdiction.
1) Did I start violating the NAP from the moment I took it out?
2) How does the effect of another jurisdiction apply to me if I have not entered into contracts with it?
3) What happens if I am a user of another jurisdiction that the first one does not recognize and simply engages in vigilantism?

A similar question: will self-ownership help if a person runs onto someone else’s field? Can I shoot them without a trial or investigation?

Beginner AnCap (question is accompanied by a donation of 0.00030432btc)

What could be called laws under ancap is the codification of successful practices. Such codes, which generalize successful practices on various topics, are in demand in a stateless society because they save effort by allowing one to avoid analyzing every case from scratch. Saving effort will mean saving money, and a cheap court, all other things being equal, will naturally win in the competitive struggle against an expensive one. But even if an expensive court provides a higher quality review of the issue, there will also be demand for a cheap one; this is a natural market segmentation by price.

Thus, by recognizing the jurisdiction of a particular company over oneself regarding a certain circle of issues, a person under ancap usually has the opportunity in advance to find out which sets of norms are used within that jurisdiction.

Furthermore, humanity has a rich experience in resolving conflicts between persons belonging to different jurisdictions. In most cases, it was a convenient practice to recognize the laws of the party on whose territory the conflict occurred. Deviations from this principle were usually stipulated separately. This could be related, for example, to the particularly important status of certain persons, or to the disputed status of the place where the conflict occurred. Thus, the concept of diplomatic immunity and international maritime law emerged.

Now let’s move directly to your questions. Let’s replace apple juice with a more understandable irritant. You brought sausage to a vegan party and began to eat it with appetite alongside the salad. Naturally, for vegans, this is a very irritating situation. And they know in advance that something like this would upset them greatly. Therefore, the party announcement usually states right away that it is a vegan party, no meat will be served, and bringing it along is prohibited. Thus, your actions violate the agreed-upon conditions of presence, and you are fully entitled to be evicted from the party.

Worse, if the announcement states that the party is vegan, no restrictions are explicitly written, you are not a vegan and do not hide it, but you were invited anyway. Respecting the hosts’ right not to serve you meat, you decide to provide for yourself—and you run into a legal conflict. Here, both the hosts, who failed to explain the rules to you, and you, who failed to understand the local defaults, are in an awkward position. Usually, such mishaps are resolved by one of the parties making concessions, but if the party hosts do not concede, you will still be evicted, because this is a place where their interpretation of disputed norms takes priority. I had a similar case during a Kupala night celebration when I started kissing a guy; it turned out he was taken, and his girl confronted me for it, which caused my bewilderment: I sincerely believed that different rules apply on Kupala night—but I yielded; the world didn’t end over that guy, basically. Similarly, our hypothetical vegans might yield to you, albeit with a sense of deep bewilderment at your tactlessness.

Now let’s move from elaborate tales to conclusions.

1. You are not obliged to follow the norms that you did not pledge to follow.
2. You may be forced to comply with them if it is a fundamental point for the enforcing party, but not for you.
3. You have the right to demand compensation for such coercion, but it is not a fact that you will receive it.
4. The more the parties are interested in future cooperation, the more likely it is that they will make mutual concessions regarding a specific current case.

In light of these theses, how can we resolve the second case, with trespassing—that is, the violation of property boundaries, even without explicit damage to that property?

1. A person is not obliged to be aware that you are against them walking across your field. It is better to put a sign on the border saying “No Trespassing,” so that the person knows that a famous Willy No-Trespassing lives here, and he is not to be trifled with (for additional reading, I recommend the well-known text about Piglet’s grandfather, floating around the internet).
2. You can force a person to leave the field if this is fundamental for you. And if they have read the sign and ignored it, you can carry out the enforcement using lethal force, without wasting time on additional persuasions.
3. Compensation may be demanded from you if, for example, there was a beaten path across your field, the boundary was not marked, the sign turned out to be unreadable and hidden in the grass, and then you pop out like a jack-in-the-box with a Winchester in hand and start shooting. State your rules in the most explicit form possible.
4. The more you are interested in future cooperation with the trespasser, the more likely it is that you will allow them on your field, even if they wandered in without permission. For example, it turned out to be a traveling salesman with a magical gift of persuasion, and now he will be your permanent supplier of tin foil hats.