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

Revision as of 19:26, 17 August 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 reward. The Bonding Curve is the clear, public math rule that gives early supporters more Rewards 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 Rewards: 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	Reward 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	Rewards 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 mathematical formula
Text-based visualization
Why a bonding curve?
Who does what
Relation to Rewards 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 Rewards generated per CHF of support. The key principle: as the reserve grows, each CHF generates fewer Rewards. 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 Rewards 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.

The mathematical formula

Rewards(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 Rewards. Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Rewards. Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Rewards.

⚠️ 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 (Rewards 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 reward 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: Rewards are not tradeable on open markets
Transparent: everyone can see the curve and calculate their Rewards

Who does what

Supporters choose when and how much to support, and can verify their Rewards 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 Rewards and Karma tokens

The bonding curve determines the total Rewards generated. The Need-Driven Funding mechanism then determines how those Rewards are split between personal Rewards and the community pool. The bonding curve itself does not determine the Cash/Karma-token ratio: that is the Need-Driven Funding mechanism's job.

Transparency commitment

WikiDeal intends to publish the full bonding curve formula, constants, and historical data. Community members would be able to verify their Reward 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|Think of the very first people who chip in to build something new: they take the biggest chance, so they get the best reward. The Bonding Curve is the clear, public math rule that gives early supporters more Rewards per franc, with no guessing and no secret deals.}}
+{{ExpertIntro|The Bonding Curve is a transparent algorithm intended to convert funding support into Rewards: 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.}}
-Wiki Core · Concept
-== The Bonding Curve ==
-Bonding Curve at a Glance
 {| class="wikitable"
@@ Line 37: / Line 32: @@
 |}
-The bonding curve is the core algorithm that converts funding contributions into Rewards. It is a '''transparent, defined algorithm''', not frozen (it can be updated through [[Gov/en/Portal:R&D/Open-Calls:Main|Open Calls]] with mathematical experts). Updates apply prospectively only: they never reduce rights already attributed at the moment of a contribution, but consistent and publicly documented. It ensures that early funders are rewarded for taking on the highest risk.
+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.
-The bonding curve ensures early funders receive more Rewards per CHF, recognizing the risk they take when the platform is unproven.
+{{ArticleSummary|
+* [[#how-it-works|How the Bonding Curve is intended to work]]
+* [[#formula|The mathematical formula]]
+* [[#visualization|Text-based visualization]]
+* [[#why-a-bonding-curve|Why a bonding curve?]]
+* [[#roles|Who does what]]
+* [[#relation|Relation to Rewards and Karma tokens]]
+* [[#transparency|Transparency commitment]]
+* [[#state-of-the-art|State of the art]]
+}}
+__NOTOC__
-=== How the Bonding Curve Works ===
+<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 Rewards generated per CHF of support. The key principle: '''as the reserve grows, each CHF generates fewer Rewards'''. This recognizes early participants and creates a natural, non-speculative incentive to support early.
-The bonding curve relates the current funding reserve level to the Rewards generated per CHF contributed. The key principle: '''as the reserve grows, each CHF generates fewer Rewards'''. This rewards early participants and creates a natural, non-speculative incentive to fund early.
+For a supporter, the experience is simple: Anna supports with CHF 100 when the reserve is nearly empty and would receive far more Rewards 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.
-=== The Mathematical Formula ===
+<span id="formula"></span>
+== The mathematical formula ==
+Rewards(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 Rewards. Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Rewards. Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Rewards.
-Rewards(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 multiplier drops) R = current reserve level (total CHF in fund) e = Euler's number (≈ 2.718...) Example at R=0 (first funder): CHF 1 → 100 Rewards Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Rewards Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Rewards
+⚠️ 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.
-⚠️ This calculation will 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.
-=== Text-Based Visualization ===
+<span id="visualization"></span>
+== Text-based visualization ==
 The relationship between reserve and multiplier (illustrative):
 Reserve (CHF) │ Multiplier (Rewards 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? ===
+<span id="why-a-bonding-curve"></span>
+== Why a bonding curve? ==
+The bonding curve addresses a fundamental bootstrapping problem: how to reward early supporters fairly without creating speculation or securities-law issues.
-The bonding curve solves a fundamental bootstrapping problem: how do you reward early funders 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
-* '''Early funders take the highest risk''' (platform unproven) → receive highest multiplier
-* '''Later funders take less risk''' (platform established) → receive lower multiplier
 * No external market price needed: the algorithm is self-contained
 * No speculation: Rewards are not tradeable on open markets
 * Transparent: everyone can see the curve and calculate their Rewards
-=== Relation to [[Gov/en/Portal:Economy/Rewards|Rewards]] and [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] ===
+<span id="roles"></span>
+== Who does what ==
+* '''Supporters''' choose when and how much to support, and can verify their Rewards 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.
+<span id="relation"></span>
+== Relation to Rewards and Karma tokens ==
+The bonding curve determines the ''total'' Rewards generated. The [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] mechanism then determines how those Rewards are split between [[Gov/en/Portal:Economy/Rewards|personal Rewards]] and the community pool. The bonding curve itself does not determine the Cash/Karma-token ratio: that is the Need-Driven Funding mechanism's job.
-The bonding curve determines the ''total'' Rewards generated. The [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] then determines how those Rewards are split between [[Gov/en/Portal:Economy/Rewards|personal Rewards]] (P2) and the community pool. The bonding curve itself does not determine the Cash/Karma-token ratio: that is the Need-Driven Funding mechanism's job.
+<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 Reward 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.
-=== Transparency Commitment ===
+<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.
-WikiDeal commits to publishing the full bonding curve formula, constants, and historical data. Community members can verify their Reward calculations independently. The formula is defined, not opaque, and any changes must go through an Open Call process with mathematical expert review.
+* 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].
-'''See also:''' [[Gov/en/Portal:Economy/Rewards|Rewards Explained]] [[Gov/en/Portal:Economy/Rewards|Rewards]] [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] [[Gov/en/Portal:Economy/Main|Why Fund WikiDeal]] [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call Guide]]
+'''See also:''' [[Gov/en/Portal:Economy/Rewards|Rewards Explained]] · [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] · [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] · [[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]]
+💡 '''Improve this concept''': submit a proposal via [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call]]
 [[Category:Migration June 2026]]
 [[Category:Innovation]]
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