Do backrun auctions protect traders? (2401.08302v1)

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.

• The paper introduces a novel laminated queueing model that explores backrun auction dynamics in batched trading systems.
• It quantifies the price manipulation coefficient to assess how arbitrageurs impact liquidity traders’ execution prices.
• The study offers actionable insights for exchange designers by outlining conditions to achieve market equilibrium and mitigate sandwiching risks.

Laminated Queueing Models for Batched Trading Venues and Market Efficiency

Introduction to Laminated Queueing Models

The paper introduces a novel 'laminated' queueing model designed for batched trading venues, particularly focusing on decentralised exchanges. This model is motivated by the need to organize Maximum Extractable Value (MEV) activity efficiently on public blockchains like Ethereum. It captures the dynamic interplay between liquidity traders and arbitrageurs within these markets, emphasizing the role of arbitrage in maintaining price equilibrium and enhancing market predictability.

Model Design and Implications

The presented model envisions a trading environment where market orders by liquidity traders interleave with orders by arbitrageurs. This interlacing, termed 'lamination,' allows arbitrage orders to follow liquidity orders in a sequence that potentially resets the marginal price to a global equilibrium. This setup aims to improve the execution predictability for liquidity traders by mitigating price manipulation risks inherently present in such trading scenarios. However, the model also acknowledges the possibility of 'blind sandwiching' by arbitrageurs, a strategy that could lead to manipulated execution prices for intervening market orders.

Numerical Results and Analysis

The paper explores the price manipulation coefficient, critical for assessing the degree of potential manipulation an arbitrageur can exert on the execution price. By introducing and analyzing this coefficient, the research delineates conditions under which the market can expect arbitrageurs to provide 'passthrough pricing', facilitating a state where each liquidity order meets the market at a state of global price equilibrium. The findings underscore scenarios where the presence of a non-negligible chance for arbitrageurs to land multiple slots could lead to manipulation, hence not fully mitigating sandwiching risks.

Theoretical Contributions

The research formalizes the structure of the laminated batch trading model, establishing the existence and convergence of equilibrium prices under certain conditions. A significant theoretical contribution is the derivation of a 'zeta function' that approximates the equilibrium price manipulation coefficient under simplifying assumptions. This equation provides a tangible method to approximate the manipulation extent, given specific market conditions and the arbitrageurs' allocation weights.

Practical Implications and Future Directions

From a practical standpoint, the model offers insights for exchange designers and participants regarding the potential limits of price manipulation, contingent on the market's liquidity structure and arbitrage opportunity allocation mechanisms. The exploration of 'per-slot pricing' points towards the flexibility and limitations of real-world systems like MEV-Blocker in relation to the model's assumptions.

While the model brings clarity to the dynamics of arbitrage and liquidity trading in batched venues, it also opens avenues for future research. Addressing assumptions like the static nature of liquidity curves, the price-taker status of the venue, and exploring the implications of limit orders and multi-block horizons could provide further depth to the understanding of market mechanisms on decentralized exchanges.

Conclusion

This paper contributes significantly to the literature on financial market microstructures by proposing a model that captures the complex interaction between arbitrageurs and liquidity traders in a batched trading environment. By assessing the conditions under which markets can achieve equilibrium pricing and identifying potential avenues for price manipulation, it lays a foundation for further empirical and theoretical exploration into efficient market designs in the context of decentralized finance.