Monopoly is just a description of a market situation. You're using it as a pejorative term without actually explaining why, in this particular case, it's a bad thing.
This works only if the two nodes in the network have exact matching needs/abilities. This is rare even in small groups.
If you will, money is a message is a message passing protocol. I don't care what's on the other side and how the message (money) was generated - all I care is that I received a message (money) and then I sent other messages (money) to other actors in the network (obviously I sent back something in exchange and so do the other nodes). Then they generated their messages and so on. This way all I need to know are the nodes immediate to me to work it out. I don't care how complex the message graph becomes, it's all irrelevant to me and to others as well. If you don't have that then you have to broadcast all that you offer and all that you need and somehow create the graph to work it out all out. Money is a cheap way of abstracting all that.