Analyzing the Economic Impact of Decentralization on Users
Amit Levy, S. Matthew Weinberg, Chenghan Zhou
TL;DR
This paper develops a theoretical framework to analyze how decentralization in a distributed ledger impacts the price users pay for blockspace. It models a two-stage game: an Upstream Tullock contest that allocates Appends, followed by a Downstream first-price auction that sells Write space to End-Users with demand D(·). The authors characterize all pure equilibria when they exist, and provide a natural, regularity-based sufficient condition for a unique market-clearing equilibrium whose existence hinges on the largest miner’s market share. They show block rewards do not alter the equilibrium price but can influence existence, offering insights into when decentralized protocols can insulate natural monopolies for patient users while leaving impatient users exposed to monopoly pricing. The results illuminate how the decentralization measure—captured by the largest miner’s share—drives prices and equilibrium viability, with implications for blockchain design and governance.
Abstract
We model the ultimate price paid by users of a decentralized ledger as resulting from a two-stage game where Miners (/Proposers/etc.) first purchase blockspace via a Tullock contest, and then price that space to users. When analyzing our distributed ledger model, we find: - A characterization of all possible pure equilibria (although pure equilibria are not guaranteed to exist). - A natural sufficient condition, implied by Regularity (a la [Mye81]), for existence of a ``market-clearing'' pure equilibrium where Miners choose to sell all space allocated by the Distributed Ledger Protocol, and that this equilibrium is unique. - The market share of the largest miner is the relevant ``measure of decentralization'' to determine whether a market-clearing pure equilibrium exists. - Block rewards do not impact users' prices at equilibrium, when pure equilibria exist. But, higher block rewards can cause pure equilibria to exist. We also discuss aspects of our model and how they relate to blockchains deployed in practice. For example, only ``patient'' users (who are happy for their transactions to enter the blockchain under any miner) would enjoy the conclusions highlighted by our model, whereas ``impatient'' users (who are interested only for their transaction to be included in the very next block) still face monopoly pricing.