Coverage Ratio

Coverage ratio r defines the system's equilibrium states.
CoverageRatio=AssetLiabilityCoverage Ratio = \dfrac{Asset}{Liability}
Liquidity provided to the protocol would become liability. A higher coverage ratio indicates a lower default risk. The coverage ratio is an important parameter to our protocol since it needs to be maintained above certain level to avoid default.
If coverage ratio < 1, the token is under-covered. And if coverage ratio > 1, it is over-covered.
Example: Coverage Ratio of USDT and USDC
In Platypus, when a swap happens, liquidity (in the system pool) for the swap-from token increases, while liquidity (in the system pool) for the swap-to token decreases.
Platypus encourages convergence towards equilibrium and penalizes the divergence from equilibrium. Therefore, we have established price slippage as a function of coverage ratio.

Slippage Function

The slippage g(r) is designed to penalize actions that deviate coverage ratios of two pools and incentivize actions that converge two coverage ratios.
Marginal Slippage (definition)
k and n are fixed parameters to be specified. Our research found that k = 0.00002 and n = 7 could be a competent choice of parameters.
Marginal Slippage (graph)
For example, if the coverage ratio is 80%, the marginal slippage is -0.08%. When a swap happens, 0.08% of the swap-to token goes to the pool.

Incentives for Convergence of Coverage Ratio

Platypus encourages convergence of coverage ratio towards 1. When a user swaps from a pool where the coverage ratio is 80%, he brings the coverage ratio of the from-token to a more healthy position. Hence he is able to receive 0.08% incentives.