Gov/en/Portal:R&D/Innovations:Bonding Curve
💡 In simple words: Think of the very first people who chip in to build something new: they take the biggest chance, so they get the best subscription token. The Bonding Curve is the clear, public math rule that gives early supporters more Subscription Tokens per franc, with no guessing and no secret deals.
🎯 In 20 seconds (scientific summary): The Bonding Curve is a transparent algorithm intended to convert funding support into Subscription Tokens: the earlier the support, the higher the multiplier (up to ×100, around ×30 at mid-stage). It is non-speculative, publicly documented, and revisable prospectively through Open Calls with mathematical experts.
| Type | Transparent algorithm |
| Purpose | Subscription Token generation from funding |
| Speculation | ❌ None |
| Covered by | Real expenses + subscriptions |
| Expert review | Open Calls (math experts) |
| Early multiplier | Up to ×100 |
| Growth multiplier | ~×30 at mid-stage |
| See also | Subscription Tokens Explained |
| See also | Why Fund WikiDeal |
Every new platform faces the same bootstrapping question: why would anyone support a project before it has proven itself? The first supporters carry the most uncertainty, so fairness suggests they should receive the most in return. The Bonding Curve is WikiDeal's answer: a public, verifiable formula that anyone can check, designed so that trust comes from transparency rather than from promises.
Summary
How the Bonding Curve is intended to work
The bonding curve relates the current funding reserve level to the Subscription Tokens generated per CHF of support. The key principle: as the reserve grows, each CHF generates fewer Subscription Tokens. This recognizes early participants and creates a natural, non-speculative incentive to support early.
For a supporter, the experience is simple: Anna supports with CHF 100 when the reserve is nearly empty and would receive far more Subscription Tokens per franc than Ben, who supports the same amount a year later when the platform is established. Both can verify their calculation themselves, because the formula is public.
No curve inside a donation: the jump comes after
There is no "curve" running inside a given donation: a donated amount does not see its multiplier decrease along the way. The multiplier applied is the one in force at the moment of the donation, for the whole amount. What the curve describes is a jump (an adjustment) recalculated after each donation, according to the Bonding Curve and the Need-Driven Funding stabilizer.
Example: if the multiplier stands at ×65, a donation of CHF 1,000 is entirely multiplied by 65 (65,000 Subscription Tokens). After the transaction, the multiplier makes a jump, for instance down to ×63.8, which applies to the next donation only.
The mathematical formula
Subscription Tokens(CHF) = CHF × multiplier(R) where multiplier(R) is a decreasing function of Reserve R: multiplier(R) = M_max × e^(-k × R). M_max = maximum multiplier (at R=0, e.g. ×100); k = decay constant (determines how fast the multiplier drops); R = current reserve level (total CHF in fund); e = Euler's number (≈ 2.718...). Example at R=0 (first supporter): CHF 1 → 100 Subscription Tokens. Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Subscription Tokens. Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Subscription Tokens.
⚠️ This calculation is intended to be discussed in Open Calls by mathematical experts. The exact constants (M_max, k) are subject to community review and may be adjusted through the Open Calls process. Updates would apply prospectively only: they would never reduce rights already attributed at the moment of a support.
Text-based visualization
The relationship between reserve and multiplier (illustrative):
Reserve (CHF) │ Multiplier (Subscription Tokens per CHF) ───────────────┼────────────────────────────── 0 │ ×100 ██████████████████████████ 5,000 │ ×80 ████████████████████ 20,000 │ ×50 █████████████ 50,000 │ ×30 ████████ 100,000 │ ×15 ████ 300,000 │ ×6 ██ 500,000+ │ ×2–5 █
Why a bonding curve?
The bonding curve addresses a fundamental bootstrapping problem: how to subscription token early supporters fairly without creating speculation or securities-law issues.
- Early supporters take the highest risk (platform unproven) → highest multiplier
- Later supporters take less risk (platform established) → lower multiplier
- No external market price needed: the algorithm is self-contained
- No speculation: Subscription Tokens are not tradeable on open markets
- Transparent: everyone can see the curve and calculate their Subscription Tokens
Who does what
- Supporters choose when and how much to support, and can verify their Subscription Tokens independently.
- Mathematical experts review the constants through Open Calls.
- The community oversees any change to the formula, which keeps governance in citizens' hands rather than in a closed boardroom.
Relation to Subscription Tokens and Karma tokens
The bonding curve determines the total Subscription Tokens generated. The Need-Driven Funding mechanism and the donor's own choice at donation time then determine how many of those Subscription Tokens the donor keeps and how much is left to the project as pure support (see the Subscription Tokens FAQ for the formulas currently proposed). Karma tokens are a separate, non-convertible form of Subscription Tokens, documented on their own page; the bonding curve does not determine them.
Transparency commitment
WikiDeal intends to publish the full bonding curve formula, constants, and historical data. Community members would be able to verify their Subscription Token calculations independently. The formula is defined, not opaque, and any change would go through an Open Call process with mathematical expert review. This reflects WikiDeal's broader aims of transparency, lower cost, flexibility and citizen participation.
State of the art
Algorithmic pricing curves and threshold-based collective funding have been studied in several strands of research. The works below provide scientific context for the bonding curve hypothesis; they do not guarantee its outcome.
- Michael Zargham, Jamsheed Shorish and Krzysztof Paruch (2019), From Curved Bonding to Configuration Spaces, WU Vienna University of Economics and Business, Working Paper Series: open access paper.
- Jiahua Xu, Krzysztof Paruch, Simon Cousaert and Yebo Feng (2023), SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols, ACM Computing Surveys, 55(11): doi:10.1145/3570639 · [{W}Automated_market_maker automated market maker on Wikipedia].
- Robin Hanson (2003), Combinatorial Information Market Design, Information Systems Frontiers, 5(1): doi:10.1023/A:1022058209073 · prediction market on Wikipedia.
- Paul Belleflamme, Thomas Lambert and Armin Schwienbacher (2014), Crowdfunding: Tapping the right crowd, Journal of Business Venturing, 29(5): doi:10.1016/j.jbusvent.2013.07.003 · crowdfunding on Wikipedia.
- Ethan Mollick (2014), The dynamics of crowdfunding: An exploratory study, Journal of Business Venturing, 29(1): doi:10.1016/j.jbusvent.2013.06.005.
See also: Subscription Tokens Explained · Subscription Tokens FAQ · Need-Driven Funding · Revenue Structure · Karma tokens · Why Fund WikiDeal · Open Call Guide
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