Estimating (Miner) Extractable Value is Hard, Let’s Go Shopping!

Abstract

The term miner extractable value (MEV) has been coined to describe the value which can be extracted by a miner, e.g., from manipulating the order of transactions within a given timeframe. $\textsc {MEV}$ has been deemed an important factor to assess the overall economic stability of a cryptocurrency. This stability also influences the economically rational choice of the security parameter k, by which a merchant defines the number of required confirmation blocks in cryptocurrencies based on Nakamoto consensus. Unfortunately, although being actively discussed within the cryptocurrency community, no exact definition of $\textsc {MEV}$ was given when the term was originally introduced. In this paper, we outline the difficulties in defining different forms of extractable value, informally used throughout the community. We show that there is no globally unique $\textsc {MEV}$/$\textsc {EV}$ which can readily be determined, and that a narrow definition of $\textsc {MEV}$ fails to capture the extractable value of other actors like users, or the probabilistic nature of permissionless cryptocurrencies. We describe an approach to estimate the minimum extractable value that would incentivize actors to act maliciously and thus can potentially lead to consensus instability. We further highlight why it is hard, or even impossible, to precisely determine the extractable value of other participants, considering the uncertainties in real world systems. Finally, we outline a peculiar yet straightforward technique for choosing the individual security parameter k, which can act as a workaround to transfer the risk of an insufficiently chosen k to another merchant.

Appendices

A Figure to Approximate $\delta$

Fig. 1.

Figure to approximate $\delta$ by comparing the average block rewards received by a miner with $p = 0.1$, to the expected infinite game rewards for the same miner with different discount factors $\delta$. All rewards are given in normalized block rewards.

B Illustration of Different Events and Their Consequences

Fig. 2.

Visual illustration of different events and their consequences on a participant with $\mathcal {R}{:}{=}\{ R_0,R_1 \}$. The total valuation of a participant before the respective event is normalized to 1. This means that the values for the initial exchange rates are $e_{0,1}=1$ (s.t. $f(r_{0,1},1)=r_{0,1}$), and that $\delta$ is static and thus ignored ($\delta _{0,1}=0$). In other words expected future rewards where already accounted for in the relation between $p_{0,1}$ and $r_{0,1}$, s.t. $p_0+r_0+p_1+r_1 = 1$.