Bonding Curve
A token bonding curve (TBC) is a mathematical curve that defines a relationship between price and token supply.
With smart contracts, we are able to move many functions into a more automated and decentralized sphere, on the blockchain, a broader range of transactions can be carried out without any human or external interference. As a consequence, blockchain protocol ecosystems to become increasingly independent, decentralized, and automated. One concept that is making waves is an automated market maker (AMM), or the token bonding curve (TBC).
In a typical TBC, the price increases as the supply of the token increases, and decreases as the supply decreases.
History
Initially conceived by Simon de la Rouviere in 2017.
Mechanics
Minting / Burning on demand
Bonding Curves use a pricing algorithm to serve as an automated market maker and provide an always available source of liquidity. Users can interact with a bonding curve by staking tokens into the bonding curve’s reserve pool. When they do so, the bonding curve mints the corresponding tokens for the user based on the pricing algorithm. The newly minted tokens can have specific utility and even be traded among users, but can always be exchanged back through the bonding curve for tokens in the bonding curve’s reserve pool.
When a token is purchased via a TBC, each subsequent buyer will have to pay a slightly higher price for each token, generating a potential profit for the earliest investors. As more people find out about the project and the buying continues, the value of each token gradually increases along the bonding curve. Early investors who find promising projects early, buy the curve-bonded token, and then sell their token back can earn a profit in the future.
Interactions
Every purchase has pushes the price up by increasing the supply, every sell has the opposite effect (unless the curve is constant). The total cost for x tokens at a given time is equal to the area under the bonding curve.
Uncapped market
A capless bonding curve is a bonding curve where no maximum token supply is specified. This means that the curve can indefinitely continue to issue new tokens when demand is there. This can be useful for markets where you wouldn’t necessarily know the upper bound of interested /organisations. For example, if you made a lottery where the ticket was a token, you don’t want to limit the number of tickets/tokens that can be sold, so instead of having a fixed token supply, you have an uncapped market.
Taxation
If you wanted to use a bonding curve as a mechanism for fundraising, you need to be able to withdraw collateral (what you pay for the tokens with) from the bonding curve. A buy tax means that you can take a percentage of the collateral for every buy and move it to a different contract/wallet, allowing you to raise money from your bonding curve without having to de-collateralize the distributed tokens. A sell tax, on the other hand, means that token holders pay a fee when they sell tokens rather than buy Lastly, one can tax both sell and buy interactions with the bonding curve contract.
Functions
A bonding curve takes ecosystem growth into consideration. It recognizes that as an ecosystem grows, so does the amount of that ecosystem’s token, and subsequently so does its value.
A bonding curve states that token and coin prices will change with their supply, either decreasing or increasing,
One can build multiple bonding curves into an ecosystem, thereby allowing for different tokens to be used for different projects, according to the functionality that the developer wants. This allows for greater versatility as different tokens can be used across different blockchains, depending on the usage of the token and the smart contracts or two-way pegs that connect the blockchains.
Types
There are four most used bonging curves:
- Sigmoid curve
- Quadratic curve
- Negative exponential curve
- Linear (non-increasing) curve
the type of the bonding curve defines the game and influences the behavior of agents.
To reward early investors: A sigmoid or quadratic bonding curve can be used. Used for projects that are expected to go viral, geared toward a large audience, ex. GameFi for games, ECOMI for NFT, or Audius for audio. The sigmoid is also used to keep costs low for early investors, while dramatically increasing the cost oncethe venture has reached critical mass or mainstream adopters (at the inflection point in the sigmoid curve). A quadratic bonding curve offers a steadier increase that is still significantly lower for early investors than latecomers.
To incentivize early investment but not disincentivize later investment: If a project requires a long period of investment, a negative exponential curve or a linear bonding curve is more suitable. A negative exponential curve creates an incentive by providing an opportunity to buy-in at a low cost. As the project gathers more interest and more investment, the curve begins to flatten, finally only having a gradual increase. A linear bonding curve will have a steady increase in cost as the project gathers more investors. A linear bonding curve is also more profitable for early investors, but there is not such a large contrast between costs for early and late investors as with the sigmoid and quadratic curves.
To keep costs continuous: A linear (non-increasing) bonding curve can be used for projects where investors are not looking to make or lose money from that investment. Here, the cost remains steady meaning no loss or profit is made. This type of bonding curve could work well for investors who are simply supporting a project that they believe in.
Augmented bonding curve
The Augmented Bonding Curve was introduced by Commons Stack (see article).