MEV Sharing with Dynamic Extraction Rates

TL;DR

The paper addresses the imbalance created by MEV extraction between users and block producers by proposing a dynamic MEV extraction-rate mechanism governed by an update rule inspired by EIP-1559. It analyzes the resulting one-dimensional dynamical system, showing convergence to an interior fixed point $\lambda^*$ for small update intensity $\eta$, potential periodic or chaotic behavior for intermediate $\eta$, and collapse to boundary states for large $\eta$, with formal conditions for market-liveness and bounded deviations. The work provides robust theoretical guarantees and extensive simulations, including burn variations and regime-switching scenarios, demonstrating that the mechanism can maintain a healthy balance and liveness even out of equilibrium. Practically, this dynamic framework informs how to enshrine MEV sharing in protocols to stabilize incentives, improve user experience, and guide future DeFi protocol design.

Abstract

Maximal Extractable Value (MEV) has emerged as a new frontier in the design of blockchain systems. In this paper, we propose making the MEV extraction rate as part of the protocol design space. Our aim is to leverage this parameter to maintain a healthy balance between block producers (who need to be compensated) and users (who need to feel encouraged to transact). We follow the approach introduced by EIP-1559 and design a similar mechanism to dynamically update the MEV extraction rate with the goal of stabilizing it at a target value. We study the properties of this dynamic mechanism and show that, while convergence to the target can be guaranteed for certain parameters, instability, and even chaos, can occur in other cases. Despite these complexities, under general conditions, the system concentrates in a neighborhood of the target equilibrium implying high long-term performance. Our work establishes, the first to our knowledge, dynamic framework for the integral problem of MEV sharing between extractors and users.

Figures (8)

• Figure 1: Bifurcation diagram for the \ref{['eq:mev_dynamics']} with respect to the adjustment intensity $\eta$ (left panel). The tolerance distributions of miners and users are shown in the panel on the right. For low values of $\eta$, the dynamics converge to $\lambda^*$ (\ref{['thm:convergence']}), whereas for large values of $\lambda$, the dynamics reach the boundary and get trapped at the corresponding fixed point (in this case $0$) in which case, the two-sided market collapses (\ref{['thm:market_liveness']}). For intermediate values of $\eta$, the dynamics are either provably chaotic (\ref{['thm:chaotic']}) or periodic with periods of difference density (\ref{['sub:periodic']}).
• Figure 2: Regions of periodic behavior for the instance of \ref{['fig:main']} and $\eta=0.6$. The panels indicate the existence of periodic points of least period $k=5$ and $k=7$, but not of $k=3$ (the period $k$ is denoted in the legends). According to \ref{['thm:sharkovsky']}, this means that for these parameters, the \ref{['eq:mev_dynamics']} have periodic points of uncountably many periods but are not provably chaotic. Similarly, we can create instances with periods of $k=4,2$ and $1$ but not of $k=8$ etc.
• Figure 3: Bifurcation diagram for the \ref{['eq:mev_dynamics']} with respect to the range of tolerance distributions. We observe here the route from chaos to order as the range of the tolerance increases.
• Figure 4: Performance of the \ref{['eq:mev_dynamics']} in the instance of \ref{['fig:main']}, cf. left panels in both Figures. The simulations use a burn-in period of $200$ iterations followed by $T=200$ iterations that are plotted in the bifurcation diagrams. The right panel shows the values of the target, $\Delta(\lambda_t)$, for each $t=201,\dots, 400$ in blue dots and the averages over this period in light-colored dots (see also the legend). As $\eta$ grows, the deviations from the target also grow till the dynamics hit the boundary and get absorbed there.
• Figure 5: In all the above simulations, we use Normal distributions for both the tolerance of users and miners on the extracted MEV rate. Specifically $F \sim \mathcal{N}(\mu = 0.4, \sigma^2=0.01)$ and $G \sim \mathcal{N}(\mu = 0.5, \sigma^2=0.01)$. In our toy example, the targeted ratio between users and miners participation is $w=1.6$.

Theorems & Definitions (20)

• proof
• Definition 1: Directionally stable fixed point
• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2: Convergence to $\lambda^*$
• proof
• Definition 2: Periodic Orbit and Points
• Definition 3: Li-York chaos Li75