Blockchain Nash Dynamics and the Pursuit of Compliance

We study Nash-dynamics in the context of 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, such as abstaining from participation and producing conflicting protocol histories. Blockchain protocols that do not lead to such infraction states are said to be compliant. Armed with this model, we evaluate the compliance of various Proof-of-Work (PoW) and Proof-of-Stake (PoS) protocol families, with respect to different utility functions and reward schemes, leading to the following results: i) PoS ledgers under resource-proportional rewards can be compliant if costs are negligible, but non-compliant if costs are significant; ii) PoW and PoS under block-proportional rewards exhibit different compliance behavior, depending on the lossiness of the network; iii) PoS ledgers can be compliant w.r.t. one infraction, i.e., producing conflicting messages, but non-compliant (and non-equilibria) w.r.t. abstaining or an attack we call selfish signing; iv) taking externalities, such as exchange rate fluctuations, into account, we quantify the benefit of economic penalties, in the context of PoS protocols, in disincentivizing particular infractions.