  Human societies engage in a number of games which use tokens as a means to
allocate, issue and access gated resources and property rights: The notion of
exchanging tokens that represent and carry value from the past into the future
to facilitate economic exchange is a fundamental concept. As agents exchange
tokens a network structure is created in which the tokens move from agent to
agent. Agents form the vertices in the network and the exchange of tokens
creates the link structure. The rules of exchange adopted collectively by
agents shape the network structure and affect the distribution of tokens
amongst agents. Many inventions including banking, payments networks and
blockchain technology have been created for the purpose of keeping accurate
records of these implicit networks. However, our formal understanding of
tokenised systems as large scale, iterative, interacting structures is limited.
The aim of this paper is to study the dynamics of token exchanges as a game,
and introduce a mathematical framework for understanding ledgers as complex
networks.
