Blockchain Nash Dynamics and the Pursuit of Compliance

TL;DR

This paper models Nash dynamics in blockchain protocols to analyze their compliance and stability, evaluating how different reward schemes and costs influence participants' incentives to follow honest protocols.

Contribution

It introduces a formal model for Nash dynamics in blockchain and assesses protocol compliance across PoW and PoS schemes under various conditions.

Findings

PoS ledgers with resource-proportional rewards are compliant if costs are negligible.

PoW and PoS protocols show different compliance behaviors based on network lossiness.

Externalities like exchange rate fluctuations can be mitigated with economic penalties.

Abstract

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.