Exploring Bonding Curve: Main Types of Automated Market Makers and Their Applications in Token Economics

Introduction

This article will compare and analyze the two main applications of Bonding Curve in the token ecosystem, which are of significant importance to the token ecosystem. We will introduce Bonding Curve as the core mechanism of Automated Market Makers (AMMs), exploring the basic concepts and differences between first-level Automated Market Makers (PAMMs) and second-level Automated Market Makers (SAMMs). This article aims to define the design space of Bonding Curve more clearly to better apply these key DeFi tools.

Overview of Bonding Curve

In recent years, Bonding Curve has gained significant attention in the Web3 field. Its application in DeFi products, such as decentralized exchanges, has fundamentally transformed the liquidity of tokens and facilitated large-scale trading of low market cap tokens. It can be said that without Bonding Curve, the development of the crypto ecosystem would not have reached today's level.

Bonding Curve is a method of mathematically encoding the relationship between two or more tokenized assets. It is implemented through smart contracts running on the blockchain, with the most basic Bonding Curve allowing these assets to trade with each other and defining their exchange rates. A common Bonding Curve equation is "X * Y = K", where the "invariant K" defines the exchange price between tokens X and Y. This "curve" defines how the price changes with variations in the supply of either token. Bonding Curves can be applied in different scenarios, providing critical infrastructure for token economic projects.

Application of Bonding Curve in Market Design

Currently, most Bonding Curves are embedded in AMMs like Uniswap, Balancer, or Curve, with the main function of facilitating the exchange of existing Tokens through "liquidity pools". These mechanisms can be viewed as SAMMs, as they are designed to facilitate secondary market trading between already existing Tokens.

Another use case of Bonding Curve is the direct issuance of Tokens ( minting ) and redemption ( burning ). These mechanisms are called PAMMs, responsible for issuing tokens when reserve assets are deposited and redeeming tokens when reserve assets are withdrawn. PAMMs enable a dynamic supply token ecosystem and serve as a "supply discovery" mechanism.

PAMMs address some key challenges faced by current Token designs, such as the necessity for projects to estimate the total number of Tokens required over their entire lifecycle. By dynamically adjusting the Token supply based on market demand, PAMMs simplify the early decision-making process and can also serve as a continuous fundraising tool, providing liquidity for promising projects and building the protocol's own liquidity.

SAMMs as a Price Discovery Mechanism

The rise of DeFi has given birth to AMM platforms such as Uniswap, Balancer, and Curve, which have replaced traditional order book trading with "liquidity pools" to achieve asynchronous swaps. These liquidity pools allow Token holders to act as "liquidity providers" by depositing Tokens into smart contracts, enabling traders to exchange assets according to the pricing algorithms set by the Bonding Curve.

This new market structure improves order book trading: they are non-custodial, asynchronous, and the fees paid by traders do not flow to intermediary exchanges, but are returned to liquidity providers.

Before the emergence of SAMMs, only a few types of tokens had sustained trading volume and liquidity. Most existing tokens were nearly untradeable, facing price discovery issues. Decentralized applications provided a platform for the easy deployment of SAMMs, enabling a large number of small-cap tokens to gain trading liquidity. SAMMs represent a significant moment in achieving product-market fit through Bonding Curves, providing price discovery and trading liquidity for most tokens.

PAMMs as a Supply Discovery Mechanism

Unlike SAMMs, PAMMs utilize Bonding Curve to facilitate the minting and burning of Tokens, providing an automated issuance and redemption mechanism for the dynamic supply of Tokens. PAMMs are a "supply discovery" tool that addresses multiple incentive misalignment issues in the design and launch process of Token ecosystems. By adjusting Token supply according to demand and keeping the deposited assets in the reserves of a smart contract, PAMMs ensure that each Token is supported by reserve assets corresponding to its redemption value.

The PAMM Bonding Curve is positioned between fixed supply and infinite supply, leveraging the advantages of both while achieving flexible expansion of supply through dynamic issuance, and simultaneously limiting supply expansion to remain consistent with the deposits of reserve assets. This enables PAMMs to provide projects with flexible Token supply to meet changing demands while maintaining the value of the Token.

The PAMMs mechanism includes two basic components:

1. Recharge Coin: Participants deposit reserve assets into the reserve pool of the PAMMs smart contract, which mints the corresponding amount of Tokens based on the price reported by the current Bonding Curve invariant and sends them to the participants.
2. Token Burn Withdrawal: Participants can destroy a portion of their tokens by selling them to the PAMM and exchanging them for reserve assets. The exchange price is determined by the Bonding Curve invariant.

Potential Benefits of Combining PAMMs and SAMMs

When PAMMs and SAMMs are combined within an ecosystem, they can provide more benefits for the Token economy. When primary issuance and secondary trading markets coexist, arbitrage opportunities arise whenever there are value discrepancies in these markets, which can be beneficial for the entire system if designed properly.

The combination of PAMMs and SAMMs in the Token ecosystem can have a "volatility suppression" effect on token prices. This effect has been observed in both models and real-time deployments, although further research is needed to understand the limitations and potential downsides of these effects.

Conclusion

Bonding Curve has become an indispensable part of the Web3 space, and its importance will continue to grow. PAMMs and SAMMs have proven their usefulness for economies of different scales. Whether launching early-stage Token ecosystems or facilitating trading in mature ecosystems, Bonding Curve will continue to play a key role in the crypto economy with its various forms and functions.

The exploration and research on Bonding Curve is still in its early stages. Although there is a lot of literature and practical applications in the field of SAMMs, PAMMs are still relatively young and not fully studied. Further exploration of the potential of these tools in addressing key challenges in the economy of crypto tokens is still needed in the future.