2024-Spring-HW2

Please complete the report problem below:

Problem 1

Provide your profitable path, the amountIn, amountOut value for each swap, and your final reward (your tokenB balance).

Solution

Output from Arbitrage.py:

path:	tokenB->tokenA->tokenD->tokenC->tokenB->tokenE->tokenD->tokenC->tokenE->tokenB

tokenB balance:	26.639970

AmountIn	AmountOut
4.999999	5.655321
5.655321	2.458781
2.458781	5.088927
5.088927	20.129888
20.129888	1.335903
1.335903	3.034864
3.034864	4.310946
4.310946	2.404817
2.404817	26.639970

Problem 2

What is slippage in AMM, and how does Uniswap V2 address this issue? Please illustrate with a function as an example.

Solution

Slippage refers to the difference between the expected price of a trade and the actual price at which the trade is executed. This discrepancy is primarily due to the impact of the trades in the pool.

Uniswap V2 addresses slippage by utilizing a constant product formula to maintain a balanced liquidity pool: $x\cdot y = k$.

Let's take the question from midterm as an example. Say at the beginning, the pool has token pairs $(9,27000)$. Assuming no other fees are present, a $(3,0)$ amountIn can have $(0,27000-\frac{9\times 27000}{12})=(0,6750)$ as amountOut. But if someone else does this transaction in advance, the $(3,0)$ amountIn could only take $(0,20250-\frac{9\times 27000}{15})=(0,4050)$ as profit, the slippage is $(0,2700)$ in total.

Problem 3

Please examine the mint function in the UniswapV2Pair contract. Upon initial liquidity minting, a minimum liquidity is subtracted. What is the rationale behind this design?

Solution

If the initial liquidity pairs were created with extremely small amounts of liquidity, slippage could possibly happen.
By imposing a minimum liquidity requirement during initial minting, Uniswap ensures that no single address (except possibly for address(0)) holds the share of the pool. And the liquidity ratio is thus bounded, which also prevents some malicious operations.

Problem 4

Investigate the minting function in the UniswapV2Pair contract. When depositing tokens (not for the first time), liquidity can only be obtained using a specific formula. What is the intention behind this?

Solution

This line of code basically tells the liquidity providers to provide liquidity per portion of different tokens in the pool; otherwise they'd have to pay more than they can get by their liquidity through burn in the future.

liquidity = Math.min(amount0.mul(_totalSupply) / _reserve0, amount1.mul(_totalSupply) / _reserve1);

The intention behind this is the to maintain the pool stability, hence reduces possible slippage.

Problem 5

What is a sandwich attack, and how might it impact you when initiating a swap?

Solution

A sandwich attack is when a blockchain attacker sandwiches a swap between two transactions to make a profit. In a sandwich attack, a malicious actor exploits the predictability of price movements at the expense of other traders. Here's how a sandwich attack typically works:

1. A user submits a swap, and it is pending confirmation.
2. A blockchain attacker sees the pending transaction, and knows the price for the token swapped will increase. So, they submit a swap. This is called front-running.
3. The blockchain attackers swap is completed at a low price.
4. The user’s transaction is completed at a high price, which means they receive less tokens than expected.
5. The blockchain attacker swaps the tokens again at a higher price. This is called back-running.

The blockchain attacker profits from the increase in price from the previous transactions. This results in a gain for the attacker, and a loss for the user.