Decentralized Equilibrium for Bitcoin Mining

Manuel Mueller-Frank, Minghao Pan and Omer Tamuz

Papers from arXiv.org

Abstract: Cryptocurrencies such as Bitcoin are defined by protocols that specify how participants record transactions and create new currency units. These protocols are not enforced by law or any central entity and instead are intended to be incentive compatible. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is known not to constitute an equilibrium (Eyal and Sirer, 2018). This leaves open the question of whether the decentralized outcome intended by Nakamoto can be sustained in equilibrium in the Bitcoin mining game. We propose inertial mining, a novel mining protocol that induces that outcome, i.e., a single longest chain in which each miner's asymptotic share of blocks equals its share of computational power. Our main result establishes that inertial mining constitutes an equilibrium, assuming no miner controls one half or more of the computational power. Inertial mining coincides with Nakamoto's protocol on the equilibrium path, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture. When a single miner controls more than half of the computational power, we show that no decentralized equilibrium exists.

Date: 2026-04, Revised 2026-08
New Economics Papers: this item is included in nep-des, nep-gth and nep-pay
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