Bonding Curve

British economist John Maynard Keynes proposed the Bancor Plan at the United Nations Monetary and Financial Conference in Bretton Woods, New Hampshire, USA, in 1944. The plan suggested that the International Settlements Union issue a unified world currency, known as the Bancor Coin, to serve as a global economic reserve currency. In homage to Keynes, the Bancor protocol was introduced in 2017, bringing the concept of collateral to the blockchain.

Presently, numerous tokens with relatively small market capitalization face challenges in being traded on centralized exchanges. The Bancor protocol addresses this issue by enabling free trading of tokens with certain collateral. This innovative approach reduces the threshold for token trading and fosters a long-tail effect within the token economy [Hertzog, E., Benartzi, G., & Benartzi, G., 2018, "Bancor Protocol Whitepaper: Continuous Liquidity and Asynchronous Price Discovery for Tokens through their Smart Contracts; aka “Smart Tokens”]. Whether functioning as a reserve currency or collateral, both concepts serve as what many consider to be a "more valuable anchor" in the realm of decentralized finance.

The bonding curve, a mathematical function connecting the supply of a digital asset to its price, serves as the backbone of token valuation, utilizing the concept of "more valuable anchor". This passive market maker mechanism, driven by the bonding curve formula, ensures that the token's price dynamically adjusts with changes in its supply [ S.D.L. Rouvière, 2017, “Tokens 2.0: Curved Token Bonding in Curation Markets”]. It is an automatic mechanism of market-making and liquidity provision in token economies, mentioned by [Zargham, M., Shorish, J., & Paruch, K., 2019, "From curved bonding to configuration spaces"].

Various forms of joint curves, such as exponential curves, convex function curves, straight lines, and aggregations of functions expressed through Taylor series expansions, fall under the umbrella of bonding curves, each with its unique characteristics.

Typically, as the token supply increases, so does its price. This design mimics real-world scenarios, like purchasing a limited asset such as Ethereum, where subsequent buyers pay a higher price. This not only embodies the passive market maker mechanism but also guarantees that every acquired token is underpinned by an anchor token, providing it with intrinsic value support. However, in specific cases, a horizontal line as a bonding curve results in a constant token price despite changes in supply. This approach finds utility in scenarios like equal-price Initial DEX Offerings (IDO) or uniform-priced concert ticket sales.

The Burve Protocol asserts that the bonding curve can yield a more "Turing complete" automated market maker (AMM) model compared to traditional order book and liquidity pool AMMs. Through extensive exploration of bonding curve theory and its application in the blockchain and DeFi sectors, Burve Protocol has unearthed innovative theoretical findings, unlocking new potential within decentralized finance.

For further theoretical insights into the Burve Protocol, please refer to the whitepaper.