I have written an academic paper called “Token Exchange Games” which develops a formal mathematical model of a ledger using a combination and of graph theory and linear algebra.
Using the research, I am able to explain crypto-token related behaviour as well as more complex behaviour within economies. I am also able to give a reasonable argument (and a formal proof) of why monetary systems evolve spontaneously. Examples of token exchange games, such as the circles crypto-token, and the lightning network are also presented. I also treat the interaction of multiple ledgers, and develop several metrics for making sense of the behaviour of agents and tokens across ledgers.
A brief summary article is presented here:
And the complete paper is presented here:
http://media.withtank.com/889e65f256/vnaicker_token_exchange_games_24_05_2018.pdf
There is still a fair amount of checking etc. to be done on the paper and I am happy to take feedback.