Dynamic Discrete Bonding Curves

Bonding curves have emerged as a powerful mechanism for managing the supply and price of tokens in a protocol. Previously, we discussed a Discrete Bonding Curve (DBC), which features constant-price regions separated by discrete price jumps. DBC combines the best features of discrete liquidity Automated Market Makers (dAMMs) like Trader Joe and Maverick Protocol and continuous bonding curves.

However, traditional DBCs are static and do not respond to changes in the protocol’s performance or changing dynamics between the protocol and its users. In this article, we introduce a new model, the Dynamic Discrete Bonding Curve (DDBC), which adjusts dynamically based on key performance indicators (KPIs) of the protocol.

Understanding DBCs

In a DBC, the price of a token is a function of its supply. The curve is divided into segments, each with a constant price. When the supply reaches the end of a segment, the price jumps to a higher level. This model provides several benefits, including price stability within each segment and predictable price increases. However, it does not consider the performance of the protocol, which can be a significant factor in the demand for its tokens.

Token distribution and sales in a DBC. Protocol captures all trading fees and offers zero slippage at constant-price levels.

Introducing Dynamic Discrete Bonding Curves

The DDBC model extends the DBC model by introducing a dynamic element based on the protocol’s KPIs. In a DDBC, the size of the price jumps and the length of the constant-price regions are determined by two (functions of) KPIs. For example, one KPI could be the protocol’s revenue (R), and the other could be the price volatility (σ) of the token.

The price increase between segments is a function of the first KPI (or a group of KPIs). A higher revenue could lead to a larger price increase, creating a direct incentive for users to contribute to the protocol’s success. The length of the constant-price regions is a function of the second KPI. The protocol may want to provide more liquidity at each price level by introducing a larger constant-price region to reduce the price volatility of its token.

A dynamic discrete bonding curve (DDBC) is projected over its continuous version. The DDBC is a bonding curve that allows an asset's price to change at predetermined times based on specific criteria. In this example, the DDBC makes an upward jump at supply levels S1 and S2 upon positive KPI results where two new logarithmic functions with higher amplitudes are discretized over |S1-S2| and |S2-S3|.

In the DDBC model, the bonding curve adjusts dynamically based on the latest KPI results. This could be done on a weekly basis, for example, with the release of the weekly KPI results. The new price function is applied prospectively, not retroactively, ensuring that the price function remains monotonically increasing and reserve assets stored in the previous supply levels remain intact.

This dynamic adjustment mechanism creates a direct link between the performance of the protocol and the price and liquidity dynamics of its token. Better performance leads to larger price increases and more available liquidity, creating strong incentives for users to contribute to the protocol’s success.

Potential Use Cases of DDBCs

Bonding curves have many use cases in the decentralized finance (DeFi) space including token launches, continuous fundraising, prediction markets, and liquidity bootstrapping. In addition to those, DDBCs support the following unique use cases:

1. Adaptive Pricing Based on Protocol Performance: DDBCs can adjust token prices based on the real-time performance of a protocol. For instance, if a protocol’s revenue increases, the price jump between segments in a DDBC might be larger. This direct link between protocol performance and token price isn’t present in traditional DBCs.
2. Liquidity Management Based on Token Volatility: The length of constant-price regions in a DDBC can be adjusted based on the price volatility of the token. If a protocol wants to reduce the price volatility of its token, it might introduce larger constant-price regions in the DDBC.
3. Time-Based Adjustments: DDBCs can be set to adjust dynamically at predetermined intervals, such as weekly, based on the release of KPI results. This allows for more frequent and adaptive adjustments compared to static DBCs.
4. Incentive Structures Tied to KPIs: DDBCs can create strong incentives for users to contribute to a protocol’s success. If the protocol performs well (based on its KPIs), users might see larger price increases and more available liquidity.
5. Dynamic Fund Allocation: In fundraising scenarios, DDBCs can adjust the allocation of funds based on the project’s milestones or KPIs. If a project meets certain performance metrics, it might receive a larger portion of the funds raised.

To summarize, the DDBC model is an innovative method that adds more flexibility and adaptability to Web3 protocols. By incorporating KPIs into the bonding curve, it enables protocols to more accurately match the token price and liquidity dynamics with their real performance. This not only improves the fairness and appeal of the protocol for users but also gives protocols a valuable tool to proactively manage their token economics based on data analysis.

Thanks a lot for reading!

You can find me on Twitter, where I write about crypto-related topics.

Disclaimer: This article is for informational purposes only and should not be considered financial or investment advice. Always do your own research and consult with a professional before making any financial decisions.