Automated Market Maker

## Automated Market Maker (AMM)
 Open Class For Certificate in Blockchain Development
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 ## `$WHOAMI`
 * DeFi developer and Web3.0 Instructor.
 * Currently,
 * Building $DINERO
 * Blockchain Instructor at York University
 * Previously, 
 * CTO and lead Blockchain Developer at opty.fi
 * Adjunct Professor at George Brown College 
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 ## Topics
 * Decentralized Finance
 * Order book based exchange
 * Decentralized Exchange
 * Constant Product AMM
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 ## Decentralized Finance
 * **DeFi**: Financial systems built with smart contracts as the platform for enforcing rules, instead of legal system
 * The intersection of economics and blockchain technology
 * Benefits are: transparent and permissionless
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 ## Trading Order book (OB)
 ![Order-book](./order_book_2.jpg)
 Image Source : https://www.ifcmarkets.com/uploads/images/order_book_2.jpg
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 ## OB fundamentals
 * Buyers/Sellers express their intent to trade by submitting bids/asks
 * These are Limit Orders (LO) with a price P and size N
 * Buy LO (P, N) states willingness to buy N shares at a price ≤ P
 * Sell LO (P, N) states willingness to sell N shares at a price ≥ P
 * OB aggregates order sizes for each unique price
 * A Market Order (MO) states intent to buy/sell N shares at the best
 possible price(s) available on the OB at the time of MO submission
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 ## OB limitations
 * Higher transaction fees and slower transaction speeds.
 * Each trade requiring on-chain validation, the underlying network’s throughput can become a bottleneck, thus affecting the overall efficiency of the exchange.
 * off-chain OB DEX have centralization risk
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 ## Decentralized Exchange
 * Platforms that facilitate peer-to-peer cryptocurrency trading without relying on intermediaries or centralized authorities.
 * Operate on blockchains, allowing users to trade directly with one another while retaining control over their private keys and funds.
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 ## Constant Product AMM
 * An AMM is a special contract that buys and sells an asset according to specific rules
 * Uniswap is most famous example on Ethereum
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 ## Constant Product Rule

* Uniswap has a simple rule: The product of the amounts of the assets is a constant
 x * y = k
 * You can swap an amount of token for another amount, but you need to keep the product the same
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 ## Constant Product Rule, 2

* Suppose there are 10 of token A and 4 of token B
 k = 10 * 4 = 40
 * The price of A in units of B is
 4 / 10 = 0.4
 * The price of B in units of A is
 10 / 4 = 2.5
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 ## Constant Product Rule, 3

* I want to buy exactly 2 units of A so I withdraw 2 A tokens from reserves, leaving 8 A tokens
 * How many Bs must there now be?
 8 * B = 40
 B = 40 / 8
 B = 5
 * Since B started at 4 tokens I need to deposit 1 unit of B to bring it up to 5
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 ## Constant Product Rule, 4

* Now there are 8 of token A and 5 of token B
 * `k` remains 40 ✓:
 k = 8 * 5 = 40
 * The price of A in units of B goes up:
 5 / 8 = 0.625
 * The price of B in units of A goes down:
 8 / 5 = 1.6
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 ## AMM implementation in Solidity 
 ```
 // SPDX-License-Identifier: MIT
 pragma solidity ^0.8.4;

// Constant Product AMM
            contract Uniswapper {
                uint256 public tokenAReserves = 10 * 1e18;
                uint256 public tokenBReserves = 4 * 1e18;

function getPriceOfA() external view returns (uint256) {
                    return (tokenBReserves * 1e18) / tokenAReserves;
                }

event AmountTokenBRequired(uint256 amount);

// e.g. buy only _amountTokenA of TokenA for any price of TokenB
                function swapTokenBForExactTokenA(uint256 _amountTokenA) external {
                    uint256 _tokenBRequired = ((tokenAReserves * tokenBReserves) /
                        (tokenAReserves - _amountTokenA)) - tokenBReserves;
                    tokenAReserves -= _amountTokenA;
                    tokenBReserves += _tokenBRequired;
                    emit AmountTokenBRequired(_tokenBRequired);
                }
            }
            ```
            ---
            ## References    
            * https://web.stanford.edu/class/cme241/lecture_slides/Tour-OrderBook.pdf
            * https://medium.com/@orderlynetwork/amms-vs-order-books-in-crypto-a-comprehensive-comparison-85e3a8afcf96