An Axiomatic Approach to Block Rewards

TL;DR

This paper develops an axiomatic framework to analyze and characterize the optimality and properties of block reward allocation rules in proof-of-work blockchains, focusing on fairness, collusion resistance, and implementation feasibility.

Contribution

It introduces an axiomatic theory for incentive-compatible reward rules, identifying conditions under which Bitcoin's proportional rule is unique and exploring alternative rules.

Findings

Bitcoin's proportional rule is uniquely optimal under certain axioms.

Many alternative reward rules can be approximately implemented.

The analysis varies with miners' risk preferences and property sets.

Abstract

Proof-of-work blockchains reward each miner for one completed block by an amount that is, in expectation, proportional to the number of hashes the miner contributed to the mining of the block. Is this proportional allocation rule optimal? And in what sense? And what other rules are possible? In particular, what are the desirable properties that any "good" allocation rule should satisfy? To answer these questions, we embark on an axiomatic theory of incentives in proof-of-work blockchains at the time scale of a single block. We consider desirable properties of allocation rules including: symmetry; budget balance (weak or strong); sybil-proofness; and various grades of collusion-proofness. We show that Bitcoin's proportional allocation rule is the unique allocation rule satisfying a certain system of properties, but this does not hold for slightly weaker sets of properties, or when the miners are not risk-neutral. We also point out that a rich class of allocation rules can be approximately implemented in a proof-of-work blockchain.