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Mechanism Design for Blockchain Order Books against Selfish Miners

Yunshu Liu, Lingjie Duan

TL;DR

This work analyzes blockchain-based order books as a dynamic game among buyers, sellers, and miners, revealing that selfish mining can induce unbounded social welfare losses (PoA). It introduces an adjustable block size (ABS) mechanism that aligns incentives by balancing throughput with the likelihood of matching desirable trades, achieving PoA 1 for NFT-like homogeneous trades and bounded PoA for heterogeneous trades. The authors provide complete-information and incomplete-information analyses, establish mixed-strategy equilibria where pure equilibria may not exist, and prove PoA bounds. They validate the approach on a local Ethereum testbed and realistic NFT/Bitcoin datasets, showing substantial social-welfare gains (up to 3.7×) over benchmarks and robust performance under random fluctuations in market participants. The results demonstrate a practical, implementable mechanism that improves welfare in decentralized order-book systems without altering core blockchain protocols.

Abstract

In blockchain-based order book systems, buyers and sellers trade assets, while it is miners to match them and include their transactions in the blockchain. It is found that many miners behave selfishly and myopically, prioritizing transactions with high fees and ignoring many desirable matches that could enhance social welfare. Existing blockchain mechanisms fail to address this issue by overlooking miners' selfish behaviors. To our best knowledge, this work presents the first analytical study to quantify and understand buyer and seller transaction fee choices and selfish miners' transaction matching strategies, proving an infinitely large price of anarchy (PoA) for social welfare loss. To mitigate this, we propose an adjustable block size mechanism that is easy to implement without altering the existing decentralized protocols and still allows buyers and sellers to freely decide transaction fees and miners to selfishly match. The analysis is challenging, as pure strategy Nash equilibria do not always exist, requiring the analysis of many buyers' or sellers' interactive mixed-strategy distributions. Moreover, the system designer may even lack information about each buyer's or seller's bid/ask prices and trading quantities. Nevertheless, our mechanism achieves a well-bounded PoA, and under the homogeneous-quantity trading for non-fungible tokens (NFT), it attains a PoA of 1 with no social welfare loss. We implement our mechanism on a local instance of Ethereum to demonstrate the feasibility of our approach. Experiments based on the realistic dataset demonstrate that our mechanism achieves social optimum for homogeneous-quantity trading like NFT. It can enhance social welfare up to 3.7 times compared to the existing order book benchmarks for heterogeneous-quantity trading of Bitcoin tokens. It exhibits robustness against random variations in buyers and sellers.

Mechanism Design for Blockchain Order Books against Selfish Miners

TL;DR

This work analyzes blockchain-based order books as a dynamic game among buyers, sellers, and miners, revealing that selfish mining can induce unbounded social welfare losses (PoA). It introduces an adjustable block size (ABS) mechanism that aligns incentives by balancing throughput with the likelihood of matching desirable trades, achieving PoA 1 for NFT-like homogeneous trades and bounded PoA for heterogeneous trades. The authors provide complete-information and incomplete-information analyses, establish mixed-strategy equilibria where pure equilibria may not exist, and prove PoA bounds. They validate the approach on a local Ethereum testbed and realistic NFT/Bitcoin datasets, showing substantial social-welfare gains (up to 3.7×) over benchmarks and robust performance under random fluctuations in market participants. The results demonstrate a practical, implementable mechanism that improves welfare in decentralized order-book systems without altering core blockchain protocols.

Abstract

In blockchain-based order book systems, buyers and sellers trade assets, while it is miners to match them and include their transactions in the blockchain. It is found that many miners behave selfishly and myopically, prioritizing transactions with high fees and ignoring many desirable matches that could enhance social welfare. Existing blockchain mechanisms fail to address this issue by overlooking miners' selfish behaviors. To our best knowledge, this work presents the first analytical study to quantify and understand buyer and seller transaction fee choices and selfish miners' transaction matching strategies, proving an infinitely large price of anarchy (PoA) for social welfare loss. To mitigate this, we propose an adjustable block size mechanism that is easy to implement without altering the existing decentralized protocols and still allows buyers and sellers to freely decide transaction fees and miners to selfishly match. The analysis is challenging, as pure strategy Nash equilibria do not always exist, requiring the analysis of many buyers' or sellers' interactive mixed-strategy distributions. Moreover, the system designer may even lack information about each buyer's or seller's bid/ask prices and trading quantities. Nevertheless, our mechanism achieves a well-bounded PoA, and under the homogeneous-quantity trading for non-fungible tokens (NFT), it attains a PoA of 1 with no social welfare loss. We implement our mechanism on a local instance of Ethereum to demonstrate the feasibility of our approach. Experiments based on the realistic dataset demonstrate that our mechanism achieves social optimum for homogeneous-quantity trading like NFT. It can enhance social welfare up to 3.7 times compared to the existing order book benchmarks for heterogeneous-quantity trading of Bitcoin tokens. It exhibits robustness against random variations in buyers and sellers.
Paper Structure (46 sections, 6 theorems, 91 equations, 17 figures, 2 tables, 2 algorithms)

This paper contains 46 sections, 6 theorems, 91 equations, 17 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivations
  3. Contributions
  4. System Model and Problem Formulation
  5. Decision models of Buyers, Sellers, and Miners in BBOB
  6. System Designer's Mechanism Design
  7. Buyers' and Sellers' Fee Decision
  8. Miners' Transaction Selection
  9. Dynamic Game Formulation among Buyers, Sellers and Miners
  10. Each Miner $m$'s Payoff
  11. Each Buyer $k$'s Payoff
  12. Each Seller $n$'s Payoff
  13. Stage II: Miner's Transaction Selection
  14. Stage I: Buyers' and Sellers' Fee Setting
  15. PoA Definition
  16. ...and 31 more sections

Key Result

Theorem 1

During mining block $t$, miner $m$'s optimal strategy is to choose the top $i^{t*}$ fee buying and selling transactions in set: where

Figures (17)

  • Figure 1: The blockchain-based order book to match buyer and seller by miners under the system designer's initially designed mechanism.
  • Figure 4: The histogram of real dataset and fitted PDF.
  • Figure 5: ABS implementation in Ethereum blockchain testbed.
  • Figure 6: Mechanism comparison for homogeneous-quantity trading.
  • Figure 7: Mechanism comparison for heterogeneous-quantity trading.
  • ...and 12 more figures

Theorems & Definitions (8)

  • Theorem 1: Miner's Optimal Strategy in Stage II
  • Definition 1: PSNE
  • Proposition 1: Buyers' and Sellers' PSNE in Stage I
  • Definition 2: MSNE
  • Proposition 2: Buyers' and Sellers' MSNE in Stage I
  • Theorem 2: PoA of current system
  • Theorem 3: PoA under ABZ
  • Theorem 4