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description: Parameterization impact on goals of the system
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# Bonding Curve Parameter Matrix & Trade-Off Decisions

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.  &#x20;

<figure><img src="https://3553550185-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FmfykzqcxD3JDEQ5bBuj1%2Fuploads%2FFRTpJ1HvhlpJxAdyEQnY%2FComplexity%20Weekend%20-%20Computer-Aided%20Governance%20in%20Web3%20Communities%20-%20Jeff%20%26%20Z%2C%20May%202021.jpg?alt=media&#x26;token=c22bc412-5d5e-480c-a788-4579b4f2aa1d" alt=""><figcaption><p>Balancing Tradeoffs in System Goals</p></figcaption></figure>

In designing any token economy, teams and communities should go through an [engineering process](https://blog.block.science/block-by-block-managing-complexity-with-model-based-systems-engineering/) including requirements gathering, which enables them to balance trade-offs and optimize for certain parameters based on engineering and business requirements. &#x20;

<figure><img src="https://3553550185-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FmfykzqcxD3JDEQ5bBuj1%2Fuploads%2Flo1U5Y0mfOeryPstTJhj%2Fimage.png?alt=media&#x26;token=58f3dcf0-d48a-4e29-99cd-ec11e174924e" alt=""><figcaption><p>Parameter configuration choices result in trade offs for system goals.  <br>(From <a href="https://app.gitbook.com/o/GnkAyEQlDelthsZ5eG3G/s/mfykzqcxD3JDEQ5bBuj1/">BlockScience</a>'s <a href="https://medium.com/block-science/how-to-perform-parameter-selection-under-uncertainty-976931ba7e5d">How to Perform Parameter Selection Under Uncertainty: Configuring Complex Systems to Handle the Real World</a>)</p></figcaption></figure>

### 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.\
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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.\
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In this video, the BCRG's Lead Researcher Jeff Emmett and Data Scientist Rohan Mehta walk us through the findings:

{% embed url="https://www.youtube.com/watch?v=CQwYXXjll0U" %}
Bonding Curve Parameterization Narrative Model Walk Through
{% endembed %}

### 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.&#x20;

<table data-full-width="true"><thead><tr><th>Parameters</th><th>Volatility</th><th>Reserve Drawdown</th><th>Maximize Fees Collected</th><th data-hidden>Return</th><th data-hidden>Control Price Magnitude</th></tr></thead><tbody><tr><td>Reserve Ratio</td><td>👆 Inversely  proportional 👇</td><td>👆 Directly proportional 👆</td><td>Non-Linear Effects ➰ </td><td>👆 Directly proportional 👆</td><td>No effect ⭕</td></tr><tr><td>Initial Supply</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>Decreases 👇</td></tr><tr><td>Initial Price</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>Increases 👆</td></tr><tr><td>Initial Reserve</td><td>👆 Inversely  proportional 👇</td><td>👆 Directly proportional 👆</td><td>No effect ⭕</td><td>Decreases 👇</td><td>No effect ⭕</td></tr><tr><td>Mint Fee</td><td>Non-Linear Effects ➰ </td><td>Non-Linear Effects ➰ </td><td>Non-Linear Effects ➰ </td><td>Increases 👆</td><td>Increases 👆</td></tr><tr><td>Burn Fee</td><td>Non-Linear Effects ➰ </td><td>Non-Linear Effects ➰ </td><td>Non-Linear Effects ➰</td><td>No effect ⭕</td><td>Decreases 👇</td></tr><tr><td>Max Supply</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>No effect ⭕</td><td>Non-Linear Effects ➰</td></tr></tbody></table>

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.&#x20;

### 🎮 Design a Bonding Curve&#x20;

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](http://172.105.101.205:5100/sim_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! 🤓).



<figure><img src="https://3553550185-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FmfykzqcxD3JDEQ5bBuj1%2Fuploads%2F8fi2JcUmQVgNFvDEWybO%2Fimage.png?alt=media&#x26;token=3b80b32a-ba5a-4f54-89a3-d429b998b2bf" alt=""><figcaption><p><a href="http://172.105.101.205:5100/sim_app">The Bonding Curve Research Group's simulation app</a></p></figcaption></figure>

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. \
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The following sections will briefly define the fundamental parameters, and look more closely at the impacts of each.
