🎛️Bonding Curve Parameter Matrix & Trade-Off Decisions

Parameterization impact on goals of the system

After extensive research, we are only beginning to scratch the surface of the massive design space of bonding curves. This is by no means an exhaustive list, however, the following section outlines some of the fundamental parameters by which bonding curves can be configured: Initial Supply, Initial Price, Initial Reserve, Reserve Ratio, Mint Fee, and Burn Fee.

The Engineering Process: Trade-Off Decisions

Ultimately, parameterization is about trade-off decision-making, where parameter sets can affect things like volatility, drawdown, returns, fees collected, etc.

Balancing Tradeoffs in System Goals

In designing any token economy, teams and communities should go through an engineering process including requirements gathering, which enables them to balance trade-offs and optimize for certain parameters based on engineering and business requirements.

Parameter configuration choices result in trade offs for system goals. (From BlockScience's How to Perform Parameter Selection Under Uncertainty: Configuring Complex Systems to Handle the Real World)

Open Source Modeling Infrastructure & Insights

The Bonding Curve Research Group is building open source modeling infrastructure for bonding curves, where live or historical data can be fed in, to simulate and learn from different data and parameterization sets. An initial modeling scope has been devised to explore the parameter selection impact of the following fundamental parameters for bonding curves:

Parameter	Description
Initial Supply	Supply of Tokens at Initialization
Initial Price	Price of Tokens at Initialization
Initial Reserve	Reserve Deposited at Initialization
Reserve Ratio	Reserve / (Price * Supply)
Mint Fee	Percentage of Deposits Collected as Fees
Burn Fee	Percentage of Redemptions Collected as Fees
Max Supply	Maximum Supply of Tokens that can be Issued

An important point to note is the relationship between supply, price, reserve, and reserve ratio which can be understood as: initial_price * initial_supply * reserve_ratio = initial_reserves. Setting any three of these parameters will determine the fourth. Based on initial models, we are beginning to understand how parameter tuning can impact a token economy. Although these are only initial results, we did uncover some insights on how these parameters can affect trade-off decisions for system goals. In this video, the BCRG's Lead Researcher Jeff Emmett and Data Scientist Rohan Mehta walk us through the findings:

Bonding Curve Parameterization Narrative Model Walk Through

Parameter Matrix

The following table indicates the effects of parameter selection on a set of common goals that a community may have regarding its token economy. The table introduces four categories of relationships: directly proportional, inversely proportional, no effect, and non-linear effects. No effect indicates an absence of a relationship between the parameter and the goal, and non-linear effects indicate that the relationship dynamics are non-linear and require more sensitive optimization analysis when making deployment decisions.

Parameters	Volatility	Reserve Drawdown	Maximize Fees Collected
Reserve Ratio	👆 Inversely proportional 👇	👆 Directly proportional 👆	Non-Linear Effects ➰
Initial Supply	No effect ⭕	No effect ⭕	No effect ⭕
Initial Price	No effect ⭕	No effect ⭕	No effect ⭕
Initial Reserve	👆 Inversely proportional 👇	👆 Directly proportional 👆	No effect ⭕
Mint Fee	Non-Linear Effects ➰	Non-Linear Effects ➰	Non-Linear Effects ➰
Burn Fee	Non-Linear Effects ➰	Non-Linear Effects ➰	Non-Linear Effects ➰
Max Supply	No effect ⭕	No effect ⭕	No effect ⭕

The above table represents preliminary results in testing the outcomes of parameter selection in a modeling environment. The analysis is not extensively rigorous as it only considers linear interactions between bonding curve-issued tokens in relation to secondary market trading.

🎮 Design a Bonding Curve

Curious about params? Try your hand at configuring a bonding curve! You can explore bonding curve parameterization in the Bonding Curve Research Group's simulation app. The app employs the narrative model with simulated data to draw insights of system behavior under different market conditions and primary-secondary market interactions. You can adjust buy/sell pressure (to simulate bull or bear market dynamics), mint and burn fees, reserve ratio, and choose the number of simulation steps to run (there is no max, only compute time! 🤓).

The Bonding Curve Research Group's simulation app

Future analysis will include extending the simulation environment to measure and monitor second-order effects of parameter selection on goal outcomes such as those above. The following sections will briefly define the fundamental parameters, and look more closely at the impacts of each.