Bonding Curve References

I have a feeling that a [bonding curve] will be the right mechanism for creating grain:$ redeemability. I’m going to start collecting valuable references on bonding curves here so that we can flow cred to the authors and explainers of bonding curves once we start using them ourselves.

Also, a big thanks to @mzargham for all of the pioneering work he’s done on bonding curves.

This post is a wiki, feel free to add more references!

Simon’s Blog Posts

Simon was one of the first people to design and implement token bonding curves on Ethereum.


A protocol that allows you to deploy a standalone bonding curve to mint your tokens and create an always available automatic market for any token.


A decentralized exchange that uses bonding curves as an automated market maker.

Aragon Fundraising

A bonding curve app for Aragon DAOs

General information


Here are a few more references to check out:

Continuous Organizations

A Javascript app for playing with Augmented bonding curve

Multidimensional bonding curve (bonding surface)

Exploring the Uniswap case by @markusbkoch


Ben Scholtz from Molecule/Protea put together a solid repo of the latest bonding curve examples here:

The Commons Stack is excited to experiment with integrations between SourceCred and the Augmented Bonding Curve, perhaps even for an early test of a cadCAD Commons for continuous funding of repo maintenance. More chats to come!


Some of this is a repeat, but since I had this list figured it would be good to share here too for people who search for “bonding curves” in the forum :slight_smile:

Bonding Curve Resources

Simon’s Blog Posts (he first person to design and implement token bonding curves on Ethereum)

Bancor (a protocol that allows you to deploy a standalone bonding curve to mint your tokens and create an always available automatic market for any token)

Uniswap (decentralized exchange that uses bonding curves as an automated market maker)

Aragon Fundraising (bonding curve app for Aragon DAOs)

General information on bonding curves

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Adding more here:

Math/Theory (my papers w/ Vienna Institute of CryptoEconomics)

Practice/Implementations (Community Inclusion Currencies Deployed bt Grassroots Economics:

As a note, I’ve had some collaborations with Grassroots economics studying their model with cadCAD as a step towards gaining broader support and scaling out CICs. One thing we did determine was that there is a mathematical equivalence between the Bancor Equations and my generalized invariant based bonding curve model in “Economic Games as Estimatiors” with the caveat that in CICs the tokens are interpreted as soft pegged to the national currency so getting non 1:1 rates is interpreted as a kind of leverage. More social and technical research is underway to reconcile theory with observed behavior in the test markets.

While I’ve done A LOT of work with Bonding Curves, I think the most important thing that I have learned is that they are not in-and-of-themselves anything, they are interfaces between economies (or maybe more appropriately economic sub-communities). The right design depends very much on the characterization of the systems being connected.

Some Examples:

  • Commons Stack: the “Augmented Bonding Curve” is designed to be an iterface between the broader ‘open-economy’ (whose unit of currency is fiat $, represented in the design by DAI or other stable token) and a community-project economy where the token being issued by the curve encodes a set of rights within the community. Initially that right is to a process which steers a funding pool, which has mechanisms related to the Bonding Curve. Slowly but surely we’re working toward a first commons deployment, the “Token Engineering Commons” is the simplest variation of the above, aiming to fund and steer rigorous research into token-design primitives. Learn more here:
  • Continuous Securities Offerings: this is an evolution of the continuous organization. This system designed by Fairmint uses a bonding curve which interfaces open-economy to a project but rather than offering decision-making rights, it essentially offers a share of future revenues through their revenue commitment mechanism. Functionally its a debt instrument. Read more here:
  • Political Action Committee: while each of the examples above use DAI or stablecoin as the bonding currency, thus interfacing with the “open-economy”, the idea of a political action committee using a bonding curve is something I’ve been brainstorming with Cem from Aragon Black. In this example, the bonded tokens are already ecosystem governance tokens such as ANT or MKR. The act of bonding them does not render them useless for governance, rather it provides a form of composable liquid democracy: the group may elect delegates to vote on behalf of the holdings of the bonding curve. See notes:

I believe this is a very fruitful space, I expect we’ll continue to see new ideas and new implementations but it will be sometime before the dynamics of such systems (specifically the social and political dynamics) are well understood.


Adding Gardens to the list since its what MetaGame plans to use for its Bonding Curve implementation!

Seems like its a better fit than Aragon Fundraising for SourceCred as well


Good list! I am obviously biased here but I agree with @mzargham that the continuous organization whitepaper would be a good fit for this list: