Measuring DEX Efficiency and The Effect of an Enhanced Routing Method on Both DEX Efficiency and Stakeholders' Benefits

TL;DR

This paper introduces STAP, a convex optimization-based metric for DEX efficiency, and demonstrates how enhanced routing algorithms can improve efficiency and stakeholder benefits, with empirical analysis on Uniswap V2 data.

Contribution

It proposes STAP as a new systematic measure of DEX efficiency and evaluates the impact of routing algorithms on efficiency and stakeholder outcomes.

Findings

STAP effectively detects arbitrage opportunities.

Enhanced routing algorithms increase DEX efficiency and trader returns.

Different algorithms impact total value locked and liquidity provider benefits.

Abstract

The efficiency of decentralized exchanges (DEXs) and the influence of token routing algorithms on market performance and stakeholder outcomes remain underexplored. This paper introduces the concept of Standardized Total Arbitrage Profit (STAP), computed via convex optimization, as a systematic measure of DEX efficiency. We prove that executing the trade order maximizing STAP and reintegrating the resulting transaction fees eliminates all arbitrage opportunities-both cyclic arbitrage within DEXs and between DEXs and centralized exchanges (CEXs). In a fully efficient DEX (i.e., STAP = 0), the monetary value of target tokens received must not exceed that of the source tokens, regardless of the routing algorithm. Any violation indicates arbitrage potential, making STAP a reliable metric for arbitrage detection. Using a token graph comprising 11 tokens and 18 liquidity pools based on Uniswap V2 data, we observe a decline in DEX efficiency between June 21 and November 8, 2024. Simulations comparing two routing algorithms-Yu Zhang et al.'s line-graph-based method and the depth-first search (DFS) algorithm-show that employing more profitable routing improves DEX efficiency and trader returns over time. Moreover, while total value locked (TVL) remains stable with the line-graph method, it increases under the DFS algorithm, indicating greater aggregate benefits for liquidity providers.