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Do backrun auctions protect traders?

Andrew W. Macpherson

TL;DR

This work proposes a laminated batch model to analyze backrun MEV on batched trading venues, formalizing how end-user orders and arbitrageur bids interleave and how this structure can enable sandwich-style price manipulation. It develops a game-theoretic framework with a lamination equation that characterizes dominant arbitrage strategies and equilibrium prices, showing conditions under which passthrough pricing emerges and providing a zeta-function approximation for the price manipulation coefficient under symmetric, blind allocations. The key contributions include existence and convergence results for equilibrium prices, a tractable closed-form surrogate for manipulation under reasonable assumptions, and a detailed exploration of how information structures and allocation mechanisms influence manipulation risk. The results offer theoretical bounds and practical insights for exchange designers aiming to limit manipulation while preserving efficient cross-venue arbitrage, with extensions to per-slot pricing, limit orders, and multi-batch dynamics.

Abstract

We study a new "laminated" queueing model for orders on batched trading venues such as decentralised exchanges. The model aims to capture and generalise transaction queueing infrastructure that has arisen to organise MEV activity on public blockchains such as Ethereum, providing convenient channels for sophisticated agents to extract value by acting on end-user order flow by performing arbitrage and related HFT activities. In our model, market orders are interspersed with orders created by arbitrageurs that under idealised conditions reset the marginal price to a global equilibrium between each trade, improving predictability of execution for liquidity traders. If an arbitrageur has a chance to land multiple opportunities in a row, he may attempt to manipulate the execution price of the intervening market order by a probabilistic blind sandwiching strategy. To study how bad this manipulation can get, we introduce and bound a price manipulation coefficient that measures the deviation from global equilibrium of local pricing quoted by a rational arbitrageur. We exhibit cases in which this coefficient is well approximated by a "zeta value' with interpretable and empirically measurable parameters.

Do backrun auctions protect traders?

TL;DR

This work proposes a laminated batch model to analyze backrun MEV on batched trading venues, formalizing how end-user orders and arbitrageur bids interleave and how this structure can enable sandwich-style price manipulation. It develops a game-theoretic framework with a lamination equation that characterizes dominant arbitrage strategies and equilibrium prices, showing conditions under which passthrough pricing emerges and providing a zeta-function approximation for the price manipulation coefficient under symmetric, blind allocations. The key contributions include existence and convergence results for equilibrium prices, a tractable closed-form surrogate for manipulation under reasonable assumptions, and a detailed exploration of how information structures and allocation mechanisms influence manipulation risk. The results offer theoretical bounds and practical insights for exchange designers aiming to limit manipulation while preserving efficient cross-venue arbitrage, with extensions to per-slot pricing, limit orders, and multi-batch dynamics.

Abstract

We study a new "laminated" queueing model for orders on batched trading venues such as decentralised exchanges. The model aims to capture and generalise transaction queueing infrastructure that has arisen to organise MEV activity on public blockchains such as Ethereum, providing convenient channels for sophisticated agents to extract value by acting on end-user order flow by performing arbitrage and related HFT activities. In our model, market orders are interspersed with orders created by arbitrageurs that under idealised conditions reset the marginal price to a global equilibrium between each trade, improving predictability of execution for liquidity traders. If an arbitrageur has a chance to land multiple opportunities in a row, he may attempt to manipulate the execution price of the intervening market order by a probabilistic blind sandwiching strategy. To study how bad this manipulation can get, we introduce and bound a price manipulation coefficient that measures the deviation from global equilibrium of local pricing quoted by a rational arbitrageur. We exhibit cases in which this coefficient is well approximated by a "zeta value' with interpretable and empirically measurable parameters.
Paper Structure (27 sections, 8 theorems, 30 equations, 1 figure)

This paper contains 27 sections, 8 theorems, 30 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Bringing order to the arbitrage market
  3. Laminated batches
  4. Passthrough arbitrage
  5. Manipulation
  6. Results
  7. Per-slot pricing
  8. Related work
  9. Exotic queue disciplines
  10. Private mempools
  11. Frequent batch auctions
  12. Future directions
  13. Acknowledgements
  14. Model
  15. Markets
  16. ...and 12 more sections

Key Result

Theorem 1.3

The marginal quote $\hat{p}$ at each slot depends only on $p_\mathcal{O}$, the marginal distributions of the trade size and direction for each $k$, and the primary and secondary allocation weights $a_{i,k},b_{i,k}$. Moreover, $\hat{p}$ converges to $p_\mathcal{O}$ as either

Figures (1)

  • Figure 1: Price evolution in a laminated batch. $I(r_i)\mathrel{\vcenter{\hbox{\scriptsize:}}\!=}$ price impact of trade $\mathtt{sell}(r_i)$.

Theorems & Definitions (40)

  • Remark 1.1: Implementations of laminated batches
  • Remark 1.2: Sybil resistance
  • Theorem 1.3: Existence and convergence of equilibrium prices, \ref{['theorem-existence']}
  • Corollary 1.4: Myopic arbitrageurs provide passthrough pricing, \ref{['theorem-myopic']}
  • Remark 1.5
  • Theorem 1.6: Zeta function approximation to manipulation coefficient, \ref{['theorem-zeta']}
  • Theorem 1.7: \ref{['theorem-multi']}
  • Definition 2.1
  • Example 2.2: CFMM
  • Example 2.3: Reference market
  • ...and 30 more