Blockchain nash dynamics and the pursuit of compliance

We study "Nash dynamics" in the context of adversarial deviations in blockchain protocols. We introduce a formal model, within which one can assess whether the Nash dynamics can lead utility-maximizing participants to defect from the "honest" protocol operation, towards variations that exhibit one or more undesirable infractions that affect protocol security, like abstaining from participation and producing conflicting protocol histories. Blockchain protocols that lead to no such infraction states are deemed compliant. Armed with this model, we evaluate the compliance of various Proof-of-Work (PoW) and Proof-of-Stake (PoS) protocol families, under different utility functions and reward schemes, leading to the following results: i) PoW and PoS protocols exhibit different compliance behavior, depending on the lossiness of the network; ii) PoS ledgers can be compliant w.r.t. one realistic infraction (producing conflicting messages) but non-compliant (hence non-equilibria) w.r.t. others (abstaining or an attack we call selfish signing); iii) considering externalities, like exchange rate fluctuations, we quantify the benefit of economic penalties in the context of PoS protocols as mitigation for particular infractions that affect protocol security.