Optimal Reward Allocation via Proportional Splitting

Abstract

Following the publication of Bitcoin's arguably most famous attack, selfish mining, various works have introduced mechanisms to enhance blockchain systems' game-theoretic resilience. The only proof-of-work reward rule with a Nash-equilibrium guarantee, FruitChains, demands reward finality on the order of days. The rules that settle in minutes have no such guarantee, and one of them, Reward Splitting, still outperforms FruitChains on most of the metrics that matter in deployment. This paper closes that gap between theory and practice. We introduce FairChain, a two-level transformation for any proof-of-work Nakamoto-style protocol. At the protocol layer, FairChain records low-difficulty samples called workshares alongside blocks. At the reward layer, it applies Proportional Reward Splitting (PRS): each height's reward is divided among the competing work objects in proportion to the intrinsic work behind them, with workshares supplying a fresh power estimate at every height. The fork-choice rule and block-production loop are left untouched, so the host chain's security carries over unchanged. Workshares can be discarded once the corresponding rewards mature, leaving zero on-chain footprint. We prove FairChain is a \r{ho}-coalition-safe {\epsilon}-Nash equilibrium for sufficiently large parameters, matching FruitChains in theory. To evaluate practical performance, we leverage Markov decision processes and compute the optimal adversarial policy under each utility function, rather than the gain of any one attack. At a six-block confirmation window, FairChain raises the deviation threshold to 38% of mining power and beats every mechanism in that framework on incentive compatibility, subversion gain (except FruitChains above 42%), and censorship susceptibility (except FruitChains below 25%).