Hi.
By “identifying actors”, if you mean that everyone who participates in the money issuing is trusted by all the network and cannot act badly, then the consensus problem you are facing is different from the problem proof-of-work blockchains solve. I’m not an expert, but I think Raft is an example of such a distributed consensus algorithm when everybody trust each other. There may be other algorithms.
If you have a network and you are ok to identify only some actors of the network, not all of them, then you may apply the consensus algorithm of Ripple : it is a distributed consensus without proof-of-work. Each node has to select a set of “miners”. These miners don’t need to be fully trusted, only not to collude with each other.