# FMM vs AMM Trading Example

**AMM Trading Model Case Description:**

In the AMM (Automated Market Maker) model example, the trading process is direct and straightforward.

1. **Initial State**:
   * The liquidity pool initially contains an equal number of two types of tokens, specifically 100 tokenA and 100 tokenB.
2. **Trading Process**:
   * A user decides to trade on the AMM platform and inputs 10 tokenA.
   * The AMM platform calculates the amount of tokenB that can be exchanged for 10 tokenA based on its core algorithm, the constant product formula (x\*y=k).
   * As a result of the formula, the user obtains 9.1 tokenB from the liquidity pool, incurring a slippage loss of 0.9 tokenA.
3. **After the Trade**:
   * Upon completing the trade, the liquidity pool updates to 110 tokenA and 90.9 tokenB, reflecting the result of the user's trade.

**FMM Trading Model Case Description:**

The FMM (Future Matching Market) model offers a more complex trading structure, including time slicing and slippage compensation mechanisms.

1. **Initial State**:
   * The liquidity pool also contains 100 tokenA and 100 tokenB.
   * The system's time slicing rule is set for 5 slices, each lasting 20 seconds.
2. **Trading Process**:
   * User A inputs 10 tokenA on the FMM platform, expecting to exchange for 10 tokenB at the current exchange rate (1 tokenA/tokenB).
   * The system receives user A's trade request, initially returning the same amount of tokens as in the AMM situation, meaning user A receives 9.1 tokenB, incurring a slippage loss of 0.9 tokenA.
   * The system further processes user A's trading intention through time slicing, dividing it into 5 slices.
3. **Time-Sliced Trade Matching**:
   * At time slice number 0, user B inputs 3 tokenB and receives 3 tokenA, while the system records a slippage compensation of 0.5 tokenA for user A. The system also processes user B's trading intention through time slicing.
   * At time slice number 1, the system dynamically adjusts prices based on current and future trading intentions. At this point, the system considers the trading intentions of user A and user B, calculating the remaining trade intentions after time slice 0 and the impact of the remaining unmatched trade intentions on the price. As a result, the liquidity pool's state changes to 101.3 tokenA and 98.7 tokenB, with 4 more unbalanced trade slices remaining.
   * User C inputs 4.8 tokenB and receives 4.92 tokenA at the new exchange rate, while the system records a slippage compensation of 0.26 tokenA for user A. The system also processes user C's trading intention through time slicing.
4. **Slippage Loss Compensation**:
   * Through trades with users B and C, user A receives slippage compensation of 0.5 tokenA and 0.26 tokenA respectively in time slices, totaling 0.76 tokenA in slippage loss compensation.
5. **After the Trade**:
   * User A successfully reduces slippage loss and completes the trade through the FMM model's system matching and time slicing processing mechanisms.

Comparing these two models, it's evident that the FMM model provides a more complex but potentially more optimized trading solution for users, especially in reducing slippage losses and addressing market fluctuations, showcasing its unique advantages.


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