  Current standards for player characterisation in tokenised state machine
replication protocols allow for honest players who will always follow the
protocol, regardless of possible token increases for deviating. Given the
ever-increasing market capitalisation of these tokenised protocols, honesty is
becoming more expensive and more unrealistic. As such, this out-dated player
characterisation must be removed to provide true guarantees of safety and
liveness in a major stride towards universal trust in state machine replication
protocols and a new scale of adoption. As all current state machine replication
protocols are built on these legacy standards, it is imperative that a new
player model is identified and utilised to reflect the true nature of players
in tokenised protocols, now and into the future. To this effect, we propose the
ByRa player model for state machine replication protocols. In the ByRa model,
players either attempt to maximise their tokenised rewards, or behave
adversarially. This merges the fields of game theory and distributed systems,
an intersection in which tokenised state machine replication protocols exist,
but on which little formalisation has been carried out. In the ByRa model, we
identify the properties of strong incentive compatibility in expectation and
fairness that all protocols must satisfy in order to achieve state machine
replication. We then provide FAIRSICAL, a protocol which provably satisfies
these properties, and by doing so, achieves state machine replication in the
ByRa model.
