Comparison of limit Order Book, amm, pmm mechanism

Limit Order Book mechanism

• peer-to-peer swap (wallstreet-like method)
• Usually off-chain
• Gnosis, dYdX

pros

1. fast

cons

1. Presence of centralized party
2. Expensive gas fee
3. Hard to bootstrap liquidity( need to have a matching buyer if you want to sell a token )

AMM(Automated Market Maker)

• peer-to-pool method
• Algorithm automatically decides price of tokens
• Uniswap , Curve, Balancer, DODO
• Constant Product Market Maker of the form \(XY = k\) is the most common AMM algorithm

pros

1. Easier liquidity provision (No need to find buyers)

cons

1. Impermanent loss and slippage occur

PMM(Proactive Market Maker)

• Invented by DODO team to reduce impermanent loss and slippage
• Onchain generalization of orderbook trading
• Utilizes oracles to gather accurate market prices. PMM use this information to estimate midprice \(i\)
• Proactively adjusts parameters such as asset ratio and curve slop
  \(P_{margin} = iR\)
  \(if\ B < B_0 \rightarrow R = 1 - k + (\dfrac{B_0}{B})^2k\)
  \(if\ Q < Q_0 \rightarrow R = 1 / (1 - k + (\dfrac{Q_0}{Q})^2k)\)
  \(else \rightarrow R = 1\)

pros

1. Better liquidity and price stability
2. Reduces barrier-to-entry for smaller projects
3. Customizable and free market making
4. Enables crowdpooling
5. Can be reversioned to AMM by setting k to 1
6. Capable of supporting stablecoin trading, as it’s virtually identical to Curve