Gov/en/Portal:R&D/Innovations:Bonding Curve: Difference between revisions

Latest revision as of 12:07, 4 October 2026

💡 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
No curve inside a donation: the jump comes after
The mathematical formula
Text-based visualization
Why a bonding curve?
Who does what
Relation to Subscription Tokens and Karma tokens
Transparency commitment
State of the art

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.

💡 Improve this concept: submit a proposal via Open Call

@@ Line 1: / Line 1: @@
-{{KidsIntro|Imagine the very first people who help build a clubhouse get the best, fairest deal — and everyone can see exactly how that deal works. The Bonding Curve is the simple, public rule that decides how much early supporters pay, with no secret discounts.}}
+{{KidsIntro|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.}}
+{{ExpertIntro|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.}}
-{{NotApproved}}
-== Bonding Curve ==
-''Innovation — WikiDeal R&D''
 {| class="wikitable"
 |-
-| Name || '''Bonding Curve'''
+| Type
+| Transparent algorithm
+|-
+| Purpose
+| Subscription Token generation from funding
+|-
+| Speculation
+| ❌ None
+|-
+| Covered by
+| Real expenses + subscriptions
+|-
+| Expert review
+| [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call]]s (math experts)
+|-
+| Early multiplier
+| Up to ×100
 |-
-| Origin || 🟠 Crypto / Token Economics
+| Growth multiplier
+| ~×30 at mid-stage
 |-
-| Category || Funding / Tokenomics
+| See also
+| [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens Explained]]
 |-
-| Status || Prototype 1 — In testing
+| See also
+| [[Gov/en/Portal:Economy/Main|Why Fund WikiDeal]]
 |}
-=== Why? What is it for? ===
+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.
+{{ArticleSummary|
+* [[#how-it-works|How the Bonding Curve is intended to work]]
+* [[#jump-after-donation|No curve inside a donation: the jump comes after]]
+* [[#formula|The mathematical formula]]
+* [[#visualization|Text-based visualization]]
+* [[#why-a-bonding-curve|Why a bonding curve?]]
+* [[#roles|Who does what]]
+* [[#relation|Relation to Subscription Tokens and Karma tokens]]
+* [[#transparency|Transparency commitment]]
+* [[#state-of-the-art|State of the art]]
+}}
+__NOTOC__
+<span id="how-it-works"></span>
+== 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.
+<span id="jump-after-donation"></span>
+== 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 [[Gov/en/Portal:Economy/Need-Driven-Funding|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.
+<span id="formula"></span>
+== 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 = [[wikipedia:E_(mathematical_constant)|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.
+<span id="visualization"></span>
+== Text-based visualization ==
+The relationship between reserve and multiplier (illustrative):
-The ''Bonding Curve'' is a mathematical mechanism that sets the purchase price of WIL (WikiDeal Investment Licences). It answers a fundamental question: how can a project reward its earliest supporters fairly, without creating speculation or opacity?
+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 █
-On conventional commercial platforms, early investors often benefit from opaque terms negotiated behind closed doors. Here, the algorithm is public, immutable and identical for everyone. The more the platform raises, the smaller the multiplier (discount) becomes — so the earliest funders get the best value, in a transparent and predictable way.
+<span id="why-a-bonding-curve"></span>
+== 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.
-This mechanism protects the community against two pitfalls: over-rewarding insiders, and devaluing later support. Trust is anchored in the mechanism itself, not in the promises of a management team.
+* '''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
-=== How does it work on WikiDeal? ===
+<span id="roles"></span>
+== Who does what ==
+* '''Supporters''' choose when and how much to support, and can verify their Subscription Tokens independently.
+* '''Mathematical experts''' review the constants through [[Gov/en/Portal:R&D/Open-Calls:Main|Open Calls]].
+* '''The community''' oversees any change to the formula, which keeps governance in citizens' hands rather than in a closed boardroom.
-In practice, each funding tranche raised corresponds to a step on the curve. In Prototype 1, the starting multiplier is high (a strong advantage for the earliest funders) and decreases progressively at each new step reached. The formula is written into WikiDeal's founding documents and cannot be changed unilaterally.
+<span id="relation"></span>
+== Relation to Subscription Tokens and Karma tokens ==
+The bonding curve determines the ''total'' [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens]] generated. The [[Gov/en/Portal:Economy/Need-Driven-Funding|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 [[Gov/en/Portal:Economy/Subscription Tokens-FAQ|Subscription Tokens FAQ]] for the formulas currently proposed). [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] are a separate, non-convertible form of Subscription Tokens, documented on their own page; the bonding curve does not determine them.
-WIL purchased through the bonding curve are then converted into Cash Rewards (via the [[Gov/en/Portal:R&D/Innovations:Funding Stabilizer|Boost]] mechanism) and into [[Gov/en/Portal:Economy/Miles-Credits|Miles Credits]]. The mechanism interacts directly with the [[Gov/en/Portal:R&D/Innovations:Annual Value Increase|5% annual value increase]]: the nominal CHF value of Credits grows each year, regardless of when they were purchased on the curve.
+<span id="transparency"></span>
+== 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.
-For funders, the bonding curve works as an explicit social contract: "here is exactly what you get, here is why, here is how it evolves." No surprises, no hidden clauses.
+<span id="state-of-the-art"></span>
+== 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.
-=== Usage level and evolution ===
+* Michael Zargham, Jamsheed Shorish and Krzysztof Paruch (2019), ''From Curved Bonding to Configuration Spaces'', WU Vienna University of Economics and Business, Working Paper Series: [https://epub.wu.ac.at/7385/ 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): [https://doi.org/10.1145/3570639 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): [https://doi.org/10.1023/A:1022058209073 doi:10.1023/A:1022058209073] · [https://en.wikipedia.org/wiki/Prediction_market prediction market on Wikipedia].
+* Paul Belleflamme, Thomas Lambert and Armin Schwienbacher (2014), ''Crowdfunding: Tapping the right crowd'', Journal of Business Venturing, 29(5): [https://doi.org/10.1016/j.jbusvent.2013.07.003 doi:10.1016/j.jbusvent.2013.07.003] · [https://en.wikipedia.org/wiki/Crowdfunding crowdfunding on Wikipedia].
+* Ethan Mollick (2014), ''The dynamics of crowdfunding: An exploratory study'', Journal of Business Venturing, 29(1): [https://doi.org/10.1016/j.jbusvent.2013.06.005 doi:10.1016/j.jbusvent.2013.06.005].
-This innovation will be tested as part of WikiDeal's Prototype 1. Its level of use and the precise deployment terms will be documented progressively as the platform evolves.
+'''See also:''' [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens Explained]] · [[Gov/en/Portal:Economy/Subscription Tokens-FAQ|Subscription Tokens FAQ]] · [[Gov/en/Portal:Economy/Need-Driven-Funding|Need-Driven Funding]] · [[Gov/en/Portal:Economy/Revenue-Structure|Revenue Structure]] · [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] · [[Gov/en/Portal:Economy/Main|Why Fund WikiDeal]] · [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call Guide]]
-----
+💡 '''Improve this concept''': submit a proposal via [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call]]
-'''See also:''' [[Gov/en/Portal:R&D/Innovations:Main|All innovations]] · [[Gov/en/Portal:R&D/Main|R&D Portal]] · [[Gov/en/Portal:Economy/Main|Economy Portal]]
+[[Category:Funding]]
+[[Category:Innovation]]