A very simplified state machine of the longest chain. The block solutions are nearly independent events which can be approximated by the Poisson distribution.

One exception is the selfish mining attack where in the longest chain rule is subjected to selfish hiding of the dominate hash power. Yet even this state machine is reasonably simple, just a few simple equations.

Whereas the state of your system is numerous agents and states. It is not yet clear to me this model can be modeled with some simplifying assumptions. Perhaps you can work with your academic researchers to see if they can.

Yet my design maintains the simple state machine of proof-of-work, while removing virtually all the bandwidth scaling restrictions. You say you can't do 100,000 transactions per second microtransactions. I can easily.