The range is a doorway
Your thing gets a band. Everything on Zwaptz inside that band is something your thing can become. Pick one, offer, and if they say yes you arrange to meet.
You are never asked what your trainers are worth, and neither is anybody else.
Not one-for-one
This is not swapping your exact thing for their exact thing
The old problem with trading things directly is that it needs a coincidence: you want theirs, they want yours, at the same moment, in the same town. That coincidence almost never happens, which is why nobody trades things.
The band removes it. You are not looking for one person who wants your trainers. You are looking at everything worth roughly what your trainers are worth, and choosing.
The band does the job money does, without anybody having to talk about money.
You see objects. Never a price tag.
The dollar figure is plumbing. It runs underneath, it decides what you are shown, and then it gets out of the way.
What you actually do is scroll through things and think I would use that. Fairness is settled by whether you want the thing in front of you, not by whether the arithmetic can be defended.

Two guitars, two different bands

An archtop and a Stratocaster, both looked after, both worth having. Neither is worth what the other is, and neither of their owners would agree on the difference.
They land in different bands, so they open onto different sets of things. That is not the system being fussy — it is the difference anybody selling either one would have to argue about for a fortnight, settled before you start.
How wide each band is, and why, is on confidence.
Bundles, when one thing is not enough
A band does not have to be filled by one object. Two of your things can reach something bigger, and you can ask for two of theirs.
An offer carries up to twelve items on the asking side, and the other person answers once for the whole thing rather than item by item.
