| Use -Case | Bonding Curve | ||
|---|---|---|---|
| Nexus Mutual | depegging with wrpped NXM | ||
Bonding curves are mathematical functions used to price and allocate digital assets in a decentralized manner. There are several ways to classify bonding curves, including:
Linear Bonding Curve: The price of the token in a linear bonding curve increases linearly as the supply of the token increases. Linear bonding curves are the simplest type of bonding curves and have a constant slope.
Concave Bonding Curve: In a concave bonding curve, the price of the token increases at a decreasing rate as the supply of the token increases. Concave bonding curves are also known as sublinear bonding curves, and they are commonly used for platforms that require a high degree of liquidity.
Convex Bonding Curve: In a convex bonding curve, the price of the token increases at an increasing rate as the supply of the token increases. Convex bonding curves are also known as super-linear bonding curves, and they are commonly used for platforms that require a high degree of scarcity.
Sigmoid Bonding Curve: A sigmoid bonding curve is a combination of a concave and convex curve, where the price of the token increases at a decreasing rate at first, then at an increasing rate, and then at a decreasing rate again. Sigmoid bonding curves are often used for platforms that require a balance between liquidity and scarcity.
Stepped Bonding Curve: A stepped bonding curve is a piecewise-linear curve with flat regions, where the price of the token remains constant for a certain range of the supply and then increases sharply. Stepped bonding curves are often used for platforms that require a high degree of liquidity at certain points in the supply curve.
Function: Bonding curves can be based on different mathematical functions, including quadratic, exponential, logarithmic, and more. The function used in the bonding curve determines how the price of the asset changes as the supply of the asset increases or decreases.
Linear Bonding Curve: The formula for a linear bonding curve is simply $y = mx + b,$ where
Exponential Bonding Curve: The formula for an exponential bonding curve is $y =$ $ab^x,$ where
Power Bonding Curve: The formula for a power bonding curve is
$y = ax^b$, where
Sigmoid Bonding Curve: The formula for a sigmoid bonding curve is $y = a / (1 + e^(-bx+c)),$ where
Hybrid Bonding Curve: The formula for a hybrid bonding curve combines multiple functions to create a more complex curve. For example, a hybrid bonding curve might use a linear function for the first portion of the curve and then switch to an exponential or power function for the later portions of the curve. The specific formula for a hybrid bonding curve depends on the combination of functions used.
$y = 0.5x + 1, x <= 1000$
$;1.5 * (1.2^(x-1000)), x > 1000$
Linear for first 1000 tokens and then exponential for all values >1000
Price determination: Price determined bonding curves are a type of bonding curve where the price of the asset is determined by the bonding curve itself. In other words, the bonding curve determines the price at which the asset can be bought or sold, based on. Bonding curves can be used to determine the price of an asset in different ways. For example, some bonding curves use a constant price function, while others use a supply-and-demand-based pricing mechanism.
Constant function bonding curve: In this type of bonding curve, the **price of the asset remains constant (**Jeff’s Carrot farm example- x tokens redeemable for “y” tokens - always ) throughout the trading period. This means that the price of the asset does not change even when there are changes in the demand and supply of the asset.
Supply and demand-based pricing bonding curve: In this type of bonding curve, the price of the asset is determined based on the supply and demand of the asset. When the demand for the asset is high, the price increases and when the demand is low, the price decreases.
Supply and demand-based pricing
$$ Price of energy = (Demand - for- energy / Supply- of- energy) + Price premium $$
Time-based pricing bonding curve: In this type of bonding curve, the price of the asset is determined based on time . The longer the asset is held, the higher the price becomes. This type of bonding curve is often used in projects that incentivize long-term holding of the asset.
Time-based pricing in Energy markets e.g Time based adjustment can be updated based on
$$ Price of energy = (Base price) + (Time-based-adjustment) $$
Weather-based pricing bonding curve: In this type of bonding curve, the price of the asset is determined based on weather conditions . For example, the price of a renewable energy token may be higher during periods of low wind or solar production, as there is a greater demand for the token during these times.
$$ Price of energy = Base price + (Weather-based- adjustment) $$
Hybrid pricing bonding curve: In this type of bonding curve, a combination of different price determination mechanisms is used to determine the price of the asset. For example, a bonding curve may use a constant price function for the first few tokens sold and then switch to a supply and demand-based pricing mechanism as more tokens are sold.
Purpose: Bonding curves can be used for different purposes, including fundraising, governance, and incentivizing behavior. For example, bonding curves can be used to raise funds for a project by selling tokens at a fixed price, or they can be used to incentivize users to participate in a decentralized platform by rewarding them with tokens.
Implementation: Bonding curves can be implemented in different ways, including on-chain and off-chain implementations. On-chain bonding curves are implemented directly on a blockchain, while off-chain bonding curves are implemented using a separate layer or protocol.
Time-based incentives: Bonding curves can be used to incentivize certain behaviors or activities over time. For example, some bonding curves offer discounts or bonuses for early adopters, while others offer rewards for long-term holders.