Blockchain Without Waste: Proof-of-Stake

47 Pages Posted: 7 Jun 2018 Last revised: 16 Jan 2019

See all articles by Fahad Saleh

Fahad Saleh

McGill University - Desautels Faculty of Management

Date Written: January 15, 2019


A blockchain constitutes a distributed ledger that records transactions across a network of agents. Blockchain's value proposition requires that agents eventually agree on the ledger's contents since payments possess risk otherwise. Restricted blockchains ensure this consensus by appointing a central authority to dictate payment validity. Permissionless blockchains (e.g. Bitcoin, Ethereum), however, admit no central authority and therefore face a non-trivial issue of inducing consensus endogenously. Nakamoto (2008) provided a temporary solution to the problem by invoking an economic mechanism known as Proof-of-Work (PoW). PoW, however, lacks sustainability, so, in recent years, a variety of alternatives have been proposed. This paper studies the most famous such alternative, Proof-of-Stake (PoS). I provide the first formal economic model of PoS and demonstrate that PoS induces consensus in equilibrium. My result arises because I endogenize blockchain coin prices. Propagating disagreement introduces illiquidity and thereby reduces blockchain coin value which implies that stake-holders face an implicit cost from delaying consensus. PoS pseudo-randomly selects a stake-holder to update the blockchain and provides her an explicit monetary incentive, a "block reward," for her service. In the event of disagreement, block rewards constitute a perverse incentive, but I demonstrate that restricting updating ability to large stake-holders induces an equilibrium in which consensus obtains as soon as possible. I also demonstrate that consensus obtains eventually almost surely in any equilibrium so long as the blockchain employs a modest block reward schedule. My work reveals the economic viability of permissionless blockchains.

Keywords: Blockchain, Consensus, Proof-of-Stake, FinTech, Cryptocurrency, Ethereum, Proof-of-Work, Bitcoin

JEL Classification: G00, G13

Suggested Citation

Saleh, Fahad, Blockchain Without Waste: Proof-of-Stake (January 15, 2019). Available at SSRN: or

Fahad Saleh (Contact Author)

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1

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