---
**paper**: https://arxiv.org/pdf/2106.07371.pdf
**title**: A 2MM: Mitigating Frontrunning, Transaction Reordering and Consensus Instability in Decentralized Exchanges
**Date**: July 23, 2021

---

# A2MM - Critique and Defects

When A2MM receives a swap transaction for a market with the assets X and Y, A2MM atomically performs optimal routing and arbitrage among the considered AMM, minimizing subsequent arbitrage transactions.

The paper actually comes to the conclusion that `batch processing` reduces MVI the most as it brings the spreads between markets closer. This principle is how A2MM works:

> It asses the size of the trade, if its enough to balance the price among the underlying liqudiity makerts it executes the trade.

**Theorem 1**: Routing optimization aims to level the
asset price on multiple AMMs and can be solved by
greedily routing transaction volume.

**Theorem 2**: An optimal strategy (Soptimal) performing routing and arbitrage among N AMMs on market (X , Y) is equivalent to a batch execution strategy (Sbatch). Sbatch consists of at most N swaps
(SwapXtoY or SwapY toX). Both Soptimal and Sbatch change the states of AMMs from
$$
\begin{array}{l}
\text {swap compression process } \\
\left(x_{1}, y_{1}, \ldots, x_{N}, y_{N}\right)\\
\text { to }\left(x_{1}^{\prime}, y_{1}^{\prime}, \ldots, x_{N}^{\prime}, y_{N}^{\prime}\right)
\end{array}
$$


[](https://i.imgur.com/8Fp9Hv7.png)

## 'Faulty' Assumptions

*specific objections to their methodology*

### Assumes only `one` DEX on chain

> In this work, we take
the stance that a blockchain should ideally only operate one
AMM smart contract, to increase the financial efficiency, reduce
network layer and block-space overhead, and consequently
increase blockchain throughput as well as security.

### Assume's that all AMM swaps initiate at the A2MM’s user interface (frontend)
They assume that all trading happens on their frontend interface

### Off chain optimization and routing
*sic*. A2MM contract with a
user interface while using Uni- and Sushiswap’s liquidity pools.
Upon receiving a swap request, A2MM derives the routing and
arbitrage parameters on the fly on-chain.

### A2MM only mitigates two-point arbitrage overhead
> 41% of the on-chain
> arbitrages are two-point arbitrages. Therefore, we estimate that A2MM will decrease about 41%

This only holds true if you assume you are the only exchange on chain, which they do assume in their paper.

### Solves Sandwhich attacks by `aggregating volume across venues`
By routing the trading volume onto multiple AMM exchanges, A2MM aggregates the MVI (minimal profitable victim input) thresholds among the underlying liquidity pools. In the simple case, where two AMM
markets have the same liquidity and pricing formula, A2MM’s
accumulative MVI threshold is 2× the MVI of a single AMM.

### Miner Network performance
Uncle rates have gone down. They dispute this fact, which makes no sense as we have seen post-Berlin block times coming down and miner profits going up (as a result of faster block times). Uncle rate has gone down, read this article by f2pool: https://medium.com/bloxroute/the-secret-weapon-f2pool-used-to-tackle-its-uncle-rate-1ecb6fe47ef8