An Axiomatic Approach to Block Rewards

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.

Improved Price Oracles

“…pair (∆ ′ , Λ ′ ) in some neighborhood around (∆, Λ), for a nonempty open set) which clearly has strictly lower objective value, so (∆, Λ) cannot be optimal for (13). So, φ ′ (R, ∆ ⋆ , Λ ⋆ ) = 0 and, therefore, that we also have (∆ ⋆ , Λ ⋆ ) ∈ T (R), so any optimal point for (13) is also feasible for (8), implying that both problems have the same optimal value.…”

“…In this case, the idea of path deficiency is extraordinarily useful: if a CFMM is path deficient, then there is no strategy by which an arbitrageur could have higher payoff than simply solving problem (8) or (9) and executing the resulting trade. Additionally, if the CFMM is strictly path deficient, then the arbitrageur only does worse by attempting to subdivide the resulting trades.…”

“…Moreover, to encourage a large swath of potential users to participate in a vote, prediction market smart contracts usually provide users with a reward. This reward is disbursed in a manner similar to how cryptocurrency rewards are given to miners and/or validators [8]. These oracles are difficult to design as one has to balance mechanism complexity with provable defenses against collusion between prediction market participants.…”

Stablecoins 2.0

“…Additionally, the setup in [11] can be extended by a network game as a stochastic dynamic system [85] or a global game [65] with noisy observations (e.g., network delay, reward expectations). Moreover, we can incorporate various assumption of risk-appetite of miners [21], selfish mining [31], and the impact of block rewards in comparison to transaction fees [20,80].…”

“…Even with small deviations, APs that arbitrage through leveraged positions can amplify the differences. 21 An ETF-like model is developed for Reserve Fund stablecoins in [54] and interpreted against Tether trading data. Models such as these are a natural starting point to address the following open questions about Reserve Fund stablecoins:…”