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# Sakai Swap

Version: Classic
SakaiSwap is the best place to trade and earn on networks such as Ethereum, Polygon, Binance Smart Chain (BSC), Avalanche, and Fantom; you can get the best rates for your token swaps and earn more with your token assets.
As DeFi's first multi-chain Dynamic Market Maker and the main protocol in Sakai Vault's liquidity hub, SakaiSwap is both a decentralized exchange (DEX) aggregator and a liquidity source with capital-efficient liquidity pools that earns fees for liquidity providers.
Unlike the static/fixed nature of a typical AMM/DEX and other liquidity platforms in the space, SakaiSwap is designed to maximize the use of capital by enabling liquidity aggregation for the best rates, extremely high capital efficiency, and reacting to market conditions to optimise returns for liquidity providers.
Utilizing a stableswap 2.0 model, Sakai Vault users can: swap stablecoins at hyper-efficient exchange rates with minimal slippage.
The swap price is defined by the rate of change in cash of asset x per change in cash of asset y. Defined as:
$exchange\ rate = \frac{\partial A_x}{\partial A_y} = \frac{1 + \frac{A}{r_x^2}}{1 + \frac{A}{r_y^2}}$
As you may have noticed, the exchange rate is independent of the number of token x and token y in the pool and depends solely on the coverage ratio.

#### Example

Assume
$A$
= 0.05,
$r_x$
= 80% and
$r_y$
= 150%. We have
$exchange\ rate = \frac{1 + \frac{0.05}{0.8^2}}{1 + \frac{0.05}{1.5^2}} \approx 1.055$
If we reverse the direction, swap from token y to token x. We have
$exchang\ rate = \frac{1 + \frac{0.05}{1.5^2}}{1 + \frac{0.05}{0.8^2}} \approx 0.95$

### Incentives for convergence of coverage ratio

Sakai Vault incentivizes a swap if the coverage ratio of two tokens is converged and penalizes if it diverges, as shown in the above example. It helps keep the pool in a healthy state and prevents a token from being defaulted.