  In cryptocurrencies, the block reward is meant to serve as the incentive
mechanism for miners to commit resources to create blocks and in effect secure
the system. Existing systems primarily divide the reward in proportion to
expended resources and follow one of two static models for total block reward:
(i) a fixed reward for each block (e.g., Ethereum), or (ii) one where the block
reward halves every set number of blocks (e.g., the Bitcoin model of halving
roughly every 4 years) but otherwise remains fixed between halvings. In recent
work, a game-theoretic analysis of the static model under asymmetric miner
costs showed that an equilibrium always exists and is unique. Their analysis
also reveals how asymmetric costs can lead to large-scale centralization in
blockchain mining, a phenomenon that has been observed in Bitcoin and Ethereum
and highlighted by other studies. In this work we introduce a novel family of
mining reward functions, HaPPY-Mine (HAsh-Pegged Proportional Yield), which peg
the value of the reward to the hashrate of the system, decreasing the reward as
the hashrate increases. HaPPY-Mine distributes rewards in proportion to
expended hashrate and inherits the safety properties of the generalized
proportional reward function. We study HaPPY-Mine under a heterogeneous miner
cost model and show that an equilibrium always exists with a unique set of
miner participants and a unique total hashrate. Significantly, we prove that a
HaPPY-Mine equilibrium is more decentralized than the static model equilibrium
under a set of metrics including number of mining participants and hashrate
distribution. Finally, we show that any HaPPY-Mine equilibrium is also safe
against collusion and sybil attacks, and explore how the market value of the
currency affects the equilibrium.
