Blockchain Nash Dynamics and the Pursuit of Compliance

We study Nash-dynamics in the context of blockchain protocols. Specifically, we introduce a formal model, within which one can assess whether the Nash dynamics can lead utility maximizing participants to defect from "honest" protocol operation, towards variations that exhibit one or more undesirable infractions, such as abstaining from participation and extending conflicting protocol histories. Blockchain protocols that do not lead to such infraction states are said to be compliant. Armed with this model, we study the compliance of various Proof-of-Work (PoW) and Proof-of-Stake (PoS) protocols, 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) considering externalities, such as exchange rate fluctuations, we quantify the benefit of economic penalties in the context of PoS protocols with respect to compliance.