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Bonding curve mechanism

PNP Exchange prices outcome tokens with a Pythagorean bonding curve—an on‑chain AMM that provides continuous liquidity from the first trade. Prices adjust smoothly with supply, so users can buy or sell without a traditional order book. Liquidity is built in, not borrowed from external market makers. We are also exploring delta‑neutral LP strategies to make providing liquidity safer.

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PNP Exchange makes liquidity mathematical.

Screenshot of a deployment confirmation message that says All checks have passed.

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The Pythagorean Formula

The total reserve calculation follows this formula: Where:
  • r is the total reserve (capital) invested in the prediction market
  • s_yes, s_no, s_draw are the supplies of YES, NO, and DRAW tokens respectively
  • c is a coefficient that starts at 1 and gradually grows to account for accrued fees
We use a modified version of the pythagorean bonding curve with the constraint that Price(yes)^2 + Price(no)^2 == 1

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How it works

  • Automatic pricing: Token prices adjust based on supply changes. More YES buys push YES up and NO down.
  • Genesis liquidity: When a market is created with initial liquidity X, the creator receives equal amounts of YES and NO backed by reserve X.

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Why bonding curves power UGC markets

Bonding curves are a cornerstone of DeFi engineering. They turn market making into code and keep markets usable from day one. We’re doubling down on advanced AMM design so USER-GENERATED-MARKETS can launch instantly, stay liquid, and scale to any niche.

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Benefits

  • Fair price discovery: Prices reflect real demand and supply
  • Sustainable economics: Trading fees accrue to the reserve and long‑term LPs

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Further reading