# Tidal Force

Tidal Force is the embedded incentive layer of Tidal AMM. It constantly incentivizes LPs in a way that moves the price of symToken/Token closer to 1. 

There are two components of Tidal Force:

* **Tidal PvP -** After LPs provide Token to Tidal AMM, the yield generated by Token (i.e., WETH for GLP) is collected by the protocol and redistributed to LPs under a new rule: **LPs with higher price orders get higher rewards**.
* **Tidal Reward -** Yield generated by leverage buyers' positions is collected by the protocol to reward LPs **who place orders above the system average price**.

### **Tidal PvP** 

Tidal PvP incentivizes LPs to place orders at higher-than-average prices to capture other LPs' yield. 

$$
\Delta R\_L=S\_L\*(1-\frac{10P\_L-9}{10P\_0-9})*A*\alpha=S\_R\*(\frac{10P\_R-9}{10P\_0-9}-1)*A*\alpha=\Delta R\_R
$$

$$
APR\_Li=\frac{10P\_Li-9}{10P\_L-9}*A*\[1-\alpha\*(1-\frac{10P\_L-9}{10P\_0-9})]
$$

$$
APR\_Rj=\frac{10P\_Rj-9}{10P\_R-9}*A*\[1+\alpha\*(\frac{10P\_R-9}{10P\_0-9})-1]
$$

where:

$$P\_0= System,average,price$$

$$S\_L=Total,liquidity,of,which,price,lower,than,P\_0$$

$$S\_R=Total,liquidity,of,which,price,higher,than,P\_0$$

$$P\_L=Weighted,average,price,of,S\_L$$

 $$P\_R=Weighted,average,price,of,S\_R$$

 $$A: Underlying  ,yield,APR,of,Token$$

 $$\Delta R\_L:PvP,loss,for,S\_L$$

$$\Delta R\_R:PvP,loss,for,S\_R$$

 $$\alpha=10^\frac{P\_R-P\_L}{1-P\_R}$$

 $$APR\_Li:APR,of,the,i\_{th},order,with,price,lower,than,P\_0$$

$$APR\_Rj:APR,of,the,j\_{th},order,with,price,higher,than,P\_0$$

### **Tidal Reward**

Tidal Reward consists of a fraction (currently set at 50%) of yield generated by all positions of leverage buyers. It is solely shared by LPs who place orders **above the system average price**. Tidal Reward received by an individual LP each block is determined by the amount of liquidity he provided and amount of staked SYM token he held: 

$$
Received,Reward,per, block=\frac{weight}{SUM(weight)}\*Tidal,Reward,per,block
$$

where:

$$
weight=min(0.4*liquidity,provided+0.6*S\_R\*\frac{staked,SYM}{SUM(staked,SYM)},liquidity,provided)
$$