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Well I'm working on a longer text on the subject, but the short version is analogous to the situation between nations with sovereign currencies. How is this trade possible if you don't only send goods but money? If there is a solution for this situation there must be something that should, at least in theory, work for individuals.
One important point is that reputation is public and that it is not isolated to one situation. But a sketch is that my own reputation is affected depending on whom i interact with. So optimally i trade with people of good intent. Good intent would be to maximize not ones own value but aim for the social optimum. This is not however possible with ordinary money since transactions are zero sum. We need a system that can handle something similar to the clark pivot.
MMT is actually a step in this direction, since allows a trusted party (the state) produce money in certain areas where we have increasing return dynamics, thus not creating inflation. It has other drawbacks though.
I'm also playing with the thought of using reported utility as trust. Since you cannot experience more than a limited amount of "happiness" per time it acts as a trust guard. That would lead to the possibility of a system that creates a utilitarian optimum. It would strike the "optimal" balance between redistribution and incentives. Long story short...
I think an economy of formalized trust or reputation is a very interesting concept. Instead of money we would interact with reputation scores or something similar. So your capital is basically your reputation or more precise your historical input to output ratio. The key aspect is that a reputation transaction is not zero sum while an economic transaction is. So i.e. releasing a patent would raise the inventors reputation without lowering reputation of the users of the idea. The economy has at its best increasing returns dynamics, but the monetary system is based on a stone age analogy of giving a X for a Y. Which is kind of weird!