An automated market maker (AMM) is a decentralized trading protocol that allows users to trade digital assets directly on a blockchain without the need for a traditional order book or an intermediary. It is a key component of decentralized finance (DeFi) platforms and has gained significant popularity in recent years.

**Who introduced Automated Market Maker (AMM)?**

The concept of AMMs was introduced by Vitalik Buterin, the co-founder of Ethereum, in 2013. The first widely adopted AMM was Uniswap, which was launched in 2018 and operates on the Ethereum blockchain. Since then, several other AMMs have emerged, each with its own unique features and variations. Read More

**Formula used by Automated Market Maker (AMM):**

AMMs rely on smart contracts to provide liquidity and facilitate trading. They utilize a mathematical formula, often based on the constant product formula, to determine the prices of assets and maintain the balance between them. The constant product formula, also known as the x*y=k formula, states that the product of the quantities of two assets in a liquidity pool should remain constant. This formula underpins the functioning of AMMs.

**How does Automated Market Maker (AMM) work?**

**Liquidity Pools:**AMMs use liquidity pools to provide liquidity for trading. Liquidity providers deposit an equal value of two different assets into a pool. For example, in a simple scenario, a liquidity pool could contain equal amounts of ETH and DAI. These pools are controlled by smart contracts and can be accessed by anyone who wants to trade.**Asset Pricing:**The prices of assets in an AMM are determined by the ratio of their quantities in the liquidity pool. According to the constant product formula, the product of the quantities of two assets must remain constant. When a trade occurs, the smart contract automatically adjusts the asset prices based on the trade size and the new quantities of assets in the pool.**Trading:**Users can trade assets by interacting directly with the AMM smart contract. They can either swap one asset for another or provide liquidity to the pool. When a user initiates a trade, the smart contract calculates the required amount of assets to complete the trade based on the current price and the desired quantity. The smart contract then executes the trade and adjusts the asset quantities in the pool accordingly.**Fees and Incentives:**AMMs usually charge a small fee on each trade, which is shared among liquidity providers as an incentive for providing liquidity. The fee helps to compensate liquidity providers for the risk they take by locking their assets in the pool. The fee can be a fixed percentage or variable based on the protocol’s design. In addition to fees, some AMMs also offer additional incentives such as governance tokens or staking rewards to attract liquidity providers.**Impermanent Loss:**Liquidity providers face the risk of impermanent loss when participating in AMMs. Impermanent loss occurs when the value of assets in the liquidity pool diverges from the value of the same assets held individually. This happens because the price of the assets in the pool changes with each trade, leading to potential temporary losses for liquidity providers. However, impermanent losses can be mitigated or offset by earning trading fees and incentives.

**Advantages of AMMs:**

AMMs offer several advantages over traditional order book-based exchanges. They provide continuous liquidity, as trades can be executed at any time without waiting for buyers or sellers to match orders. AMMs are also permissionless, allowing anyone to participate in trading or provide liquidity without the need for intermediaries or centralized control. Furthermore, AMMs enable direct peer-to-peer trading, reducing counterparty risk and lowering costs.

**Limitations and Challenges:**

AMMs have certain limitations and face challenges. The most significant challenge is the high cost of transactions and scalability issues on some blockchains. As transaction fees rise during periods of network congestion, trading on AMMs can become expensive. Improving scalability and reducing fees are ongoing research areas to address these challenges. Additionally, the reliance on mathematical formulas for asset pricing makes AMMs less suitable for illiquid or volatile assets that may require more sophisticated market mechanisms.

**How does the mathematical formula work? **

The mathematical formula commonly used by automated market makers (AMMs) to determine prices is known as the constant product formula. This formula ensures that the product of the quantities of tokens in the liquidity pool remains constant, even as the supply and demand of the tokens change. The most well-known implementation of the constant product formula is the Automated Market Maker (AMM) called Uniswap.

The constant product formula is expressed as:

x * y = k

Where:

- x is the quantity of the first token in the liquidity pool.
- y is the quantity of the second token in the liquidity pool.
- k is a constant value.

To understand how this formula works, let’s consider an example using ETH and DAI as the trading pair in the liquidity pool.

Suppose the initial liquidity provider deposits 1 ETH and 1000 DAI into the pool. The product of the quantities of tokens in the pool (x * y) would be:

1 ETH * 1000 DAI = 1000 ETH * DAI

Let’s say a trader wants to swap 0.1 ETH for DAI. The AMM uses the constant product formula to calculate the new quantity of DAI (y) based on the existing quantity of ETH (x) and the constant (k). The formula becomes:

(x + d) * (y – D) = k

Where:

- x is the initial quantity of ETH (1 ETH).
- y is the initial quantity of DAI (1000 DAI).
- d is the amount of ETH deposited by the trader (0.1 ETH).
- D is the amount of DAI received by the trader.

To calculate D, we rearrange the formula:

D = y – ((x * y) / (x + d))

Plugging in the values:

D = 1000 DAI – ((1 ETH * 1000 DAI) / (1 ETH + 0.1 ETH))

D = 1000 DAI – (1000 DAI / 1.1)

D = 1000 DAI – 909.09 DAI

D ≈ 90.91 DAI

So, the trader would receive approximately 90.91 DAI in exchange for 0.1 ETH.

Importantly, as the trader swaps tokens, the quantities in the pool change, but the constant value (k) remains the same. This means that the ratio of tokens in the liquidity pool adjusts to reflect the relative supply and demand. As more trades occur, the price of the tokens is determined by the balance of the quantities in the pool.

**Conclusion**

AMMs provide an innovative way to trade cryptocurrencies by leveraging liquidity pools and mathematical formulas to determine prices. They allow for decentralized and permissionless trading, as users can interact with the AMM protocols using their cryptocurrency wallets. AMMs have played a vital role in the growth of DeFi, offering users more control over their funds and contributing to the development of a more inclusive and accessible financial ecosystem.

It’s worth noting that the AMM space is evolving rapidly, and new variations and improvements are being introduced regularly. This explanation provides a foundational understanding of AMMs, but there may be specific nuances and advanced concepts that exist beyond the scope of this overview.