The Riddles way
I don't know any existing models that require no physical props and allow a 1v1 Willpower duel. However, I know a very interesting model that was used for torture rules at one Witcher LARP hosted in Saint-Petersburg.
To be short, the attacker has a prepared riddle that the defender needs to solve in a given time frame. If a riddle is solved, the attack has failed. If the riddle is not solved, the attack is successful and, in the case of that model, the victim has to answer a question.
An important fact: the answer given does not have to copy the intended one, it can be anything that matches the riddle! You can add a rule that if the question is not answered, the attacker needs to name the answer to prove that it actually even exists (if you don't trust your players).
If you need a 1v1 duel, you can simply switch the attacker and the defender and choose your own consequences of a failed round. You can even try to change them based on how much time the riddle takes!
In any case, test your system before you use it. Ask some of your players to perform the duels of minds by your new rules.
- No props at all!
- A pure duel of minds, no physical contest involved!
- A bunch of riddle need to be prepared beforehand.
- A gamemaster needs to check the prepared riddles to prove that they fit in the setting well, are answerable, not too difficult etc.
- The victims need time to make an answer, such a duel is not quick. You can play with the riddle difficulty and time, but it won't be resolved in 15 seconds like a swordfight.
The Associations way
This one was used at one Harry Potter LARP for the simulation of Legilimency and Occlumency. Note that this mechanic will only work for interrogation, while the previously listed one will just yield you a winner and a loser and let you choose the consequences.
We used Telegram for this so that others cannot perceive what's happening, it was not allowed to show what you write and get in this messenger.
The attacker pronounces a magical word to announce the use of spell, and has to write some keywords. The maximum amount of them depends on their experience at the use of Legilimency (the more powerful they are, more words they can write). The victim has to write up to 7 words that their character associates with the keywords sent by the attacker, but only a given amount of them has to be true.
The victim has 3 minutes to think.
For example, Alice (Legilimency level 3) attacks Bob (Occlumency allows to send only 2 real associations). Alice thinks that Bob killed Charlie yesterday when they were alone, and says: "Charlie, murder, yesterday". Bob did kill Charlie, and has to say at least two things that applied to this time and are connected with ALL THREE WORDS sent/said by Alice, for example, "Moonlight, Fear". But there are 5 more slots to fill with lies, as Bob is great at hiding the reality! So, Bob sends: "Moonlight, Fear, Kiss, Together forever, Way to home". 2 more slots left, but Bob probably wants to hide the ability to mask the truth, and fakes having to send 5 pieces of data.
- Is fun!
- Is a challenge of minds.
- You can still make stats influence that.
- Is waaay to slow.
- Requires a smartphone with internet access. You can try to do it by pieces of paper -- then you actually need props, though very easy props. You can try it by voice, but then others can hear what's happening unless you whisper.
- The model is complicated. You will probably have to host a masterclass on this before your game starts so that players understand how it actually works.