Exploring Bonding Curve: Comparing the Application of PAMMs and SAMMs in Token Economy

原文：《Exploring Bonding Curves: Differentiating Primary and Secondary Automated MarketMakers》

作者：Jeff Emmett，CuriousRabbit.eth & Jessica Zartler

Compilation: Sissi

Preface

**This article will compare two different applications of Bonding Curve in the token ecosystem, which have important functions for the token ecosystem. **At the same time, we will also introduce Bonding Curve as the core mechanism of automated market makers (AMMs), and discuss Primary Automated Market Makers (hereinafter referred to as "PAMMs") and Secondary Automated Market Makers The basic concepts of Market Makers (hereinafter referred to as "SAMMs") and the differences between them. The goal of this paper is to more clearly define the design space of the Bonding Curve so that these key DEFI tools can be applied more responsibly.

*Note: The terms SAMMs and PAMMs were originally coined by researchers using Gyroscope, an algorithmic stablecoin built with them.

Part.1 Bonding Curve Overview

In recent years, in the field of Web3, Bonding Curve has been a topic that attracts attention. Their application in DeFi products, such as decentralized exchanges, has revolutionized token liquidity and facilitated large-scale trading of small-cap tokens. It can be said that without Bonding Curve, the development of the encryption ecosystem would not be able to achieve today's achievements. While many token ecosystems take advantage of these tools, how Bonding Curves work and why they matter remain a mystery to most users.

So, what is Bonding Curve? **Bonding Curve is a method of mathematically encoding the relationship between two or more tokenized assets. **Initiated through smart contracts running on the blockchain, the initial and most basic Bonding Curve allows these assets to be traded with each other, and their exchange ratios are defined through the Bonding Curve. A common Bonding Curve equation is "X * Y = K", where the "invariant K" defines the exchange price between token X and token Y. This "curve" defines how the price changes as the supply of any token increases or decreases. **Bonding Curve can be applied to different scenarios and configurations, providing key infrastructure for projects deploying token economy. **

Here is a graph of how two tokens are related to each other via the Bonding Curve. Different "shapes" of the Bonding Curve can result in mechanisms with different properties, which may be helpful for different situations and usage scenarios.

Since Bonding Curves are essentially a mathematical function, it can be difficult to understand how they can have such a dramatic impact on the token ecosystem. However, when these mathematical relationships are encoded into smart contracts, they lay the economic foundation for solving some of the main challenges of distributed economic systems, such as enabling small economies, providing the necessary transaction liquidity, and facilitating the dynamic adjustment of tokens according to demand. supply. By embedding Bonding Curves in smart contracts, we can create novel and meaningful market structures with customizable design spaces.

Part.2 Bonding Curve applied to market design

Currently, most Bonding Curves are embedded into AMMs like Uniswap, Balancer, or Curve, and their main function is to facilitate the exchange of existing tokens through "liquidity pools". These mechanisms can be considered SAMMs**, as their purpose is to facilitate secondary market transactions between tokens that already exist. There have been many articles about the application of Bonding Curve in this area, and many different invariant functions have been experimented with for various purposes.

The diagram above shows a basic AMM as a trader exchanging between two assets. AMM utilizes different types of Bonding Curves to determine the price relationship between tokens.

Another use case for Bonding Curve is the direct issuance (minting) and redemption (burning) of ** tokens. These mechanisms can be referred to as PAMMs** because they are responsible for the issuance of tokens when the reserve assets are deposited, and the exchange of tokens when the reserve assets are withdrawn. PAMMs enable a dynamically provisioned token ecosystem and can be viewed as a "supply discovery" mechanism for tokens deployed using these tools.

PAMMs address some of the key challenges faced by current token designs, such as projects having to guess how many tokens the system will need throughout its lifetime. By allowing dynamic adjustment of token supply according to market demand, **PAMMs not only simplify the early decision-making process, but also serve as a continuous fundraising tool to provide liquidity for potential projects, thereby building the protocol's own liquidity **.

The following will briefly introduce the application cases of these two Bonding Curves to understand the benefits they bring to the token ecosystem, and briefly explore how they can be combined to provide important infrastructure for token ecosystems of all sizes.

Part.3 SAMMs as a Price Discovery Mechanism: Preliminary Product Market Fit

The rise of DeFi has given rise to AMM platforms such as Uniswap, Balancer, and Curve, which replace traditional order book transactions with "liquidity pools" that enable asynchronous swaps. These liquidity pools allow token holders to act as "liquidity providers" to deposit selected tokens into smart contracts so that traders can easily exchange assets according to the pricing algorithm set by Bonding Curve.

The novel market structure improves order book transactions in several ways: they are non-custodial (since there is no need for an exchange to hold user funds on behalf of them), they are asynchronous (since buy and sell orders do not need to be directly matched, but instead enter liquidity pools ), and most importantly, the fee paid by the trader will not flow to the intermediary exchange, but will be returned to the liquidity provider itself.

Before SAMMs, only Bitcoin, Ethereum, and a handful of other tokens had consistent transaction volume (and thus transaction liquidity). Most existing tokens are barely tradable and there are many price discovery issues due to low trading volume and depth. Decentralized applications (such as Uniswap) provide platforms for the easy deployment of SAMMs, enabling a large number of small market cap tokens to obtain a certain degree of trading liquidity. SAMMs are an important moment for Bonding Curve to achieve PMF, providing price discovery and trading liquidity for most tokens. It is believed that there will be more similar developments in the future.

Image credit: @CuriousRabbit

Part.4 PAMMs as Supply Discovery Mechanism: The Power of Dynamic Token Issuance

Let's say you want to run a theme park, but before you start operating, you need to determine the number of rides you need to satisfy customer demand over the next 15 years. Sounds nearly impossible right? However, this is not much different from how most tokens are issued today, with development teams setting pre-defined token issuance schedules, some spanning hundreds of years. However, with PAMMs, token ecosystem designers no longer need to guess how many tokens their ecosystem will need and how fast they will grow. Unlike SAMMs, PAMMs utilize Bonding Curves to facilitate the minting and burning of tokens, thereby providing an automated issuance and redemption mechanism for the dynamic supply of tokens.

PAMMs are a “supply discovery” tool (as opposed to the “price discovery” function of SAMMs) that addresses multiple incentive mismatches that can exist in token ecosystem design and launch. By adjusting token supply according to global demand, and keeping deposited assets in reserves in automated smart contracts, PAMMs ensure that each token is backed by reserve assets corresponding to its redemption value. **

**Why should tokens be issued dynamically? **

Most tokens released today tend to fall between two extremes: from a fixed supply to an infinite supply. Both distribution models have their own advantages and disadvantages, and are used in different situations for different reasons. A fixed-supply token can provide holders with some assurance that the token will not dilute its value through additional issuance, however the rigidity of a fixed supply can limit the ability of the ecosystem to respond to new demands on the network. On the other hand, an unlimited supply of tokens could incentivize staking-like behavior by providing token rewards, but increasing the unlimited supply could dilute existing token holders and over time Reduce trust in the token, especially if the productivity of the network (and token price) does not grow with the supply.

PAMM Bonding Curve is in the middle between these two extremes. It not only takes advantage of the advantages of fixed supply and unlimited supply, but also realizes the flexible expansion of supply through dynamic issuance, but at the same time limits the expansion of supply and maintains a balance with the deposit of reserve assets. unanimous. This enables **PAMMs to provide projects with a flexible token supply to meet growing (or decreasing) demand while maintaining token value. **

Dynamic issuance enables the token supply to expand as demand for a particular service grows, while ensuring that each token in the supply is pegged to an asset in a certain percentage, a guarantee built into the PAMMs issuance mechanism via the Bonding Curve invariant .

The PAMMs mechanism consists of two basic parts:

• Recharge minting coins**: **Participants deposit reserve assets (such as $USDC or $ETH) into the reserve pool of the PAMMs smart contract, and the contract mints a corresponding amount of coins according to the price reported by the current Bonding Curve invariant tokens and send them to participants.
• **Destruction withdrawal: **Participants can destroy part of the tokens by selling them to PAMM and converting them into reserve assets (such as $USDC or $ETH). This exchange price is determined by the Bonding Curve invariant.

Image credit: @CuriousRabbit

Today, multiple PAMMs exist in practice, although there can be significant differences in terminology and customization between groups using these tools. To better understand the strengths and weaknesses of these mechanisms in real-world deployments, the Bonding Curve research group set out to conduct various case studies of tools like PAMMs. The goal of the research is to expand the discussion on these curve design and configuration best practices, providing useful guidance to others. At the same time, efforts are also being made to build data structures for analytical modeling and simulation of these new tools and to share lessons learned in practical applications.

Part.5 Potential benefits of combining PAMMs with SAMMs

Leaving aside the specific mechanism of PAMMs and SAMMs, when they are combined in an ecosystem, these tools can provide more benefits to the token economy. When both primary issuance and secondary trading markets exist, arbitrage opportunities arise whenever the values of these markets diverge, which can be beneficial to the system as a whole if designed properly.

If the token price on SAMMs is higher than the minting price on PAMMs, any participant can mint new tokens on PAMMs by depositing reserve assets, thereby increasing token supply and (price) on the primary market. They can then sell these tokens on SAMMs at a higher price than they just bought them, thereby lowering token prices on the secondary market. This behavior helps to adjust the two market prices to demand by increasing token supply, with arbitrageurs receiving the difference for their corrective action of increasing token supply.

The reverse is also true, if tokens are trading at a lower price on SAMMs than the burn price on PAMMs, anyone can buy these lower priced tokens in the secondary market, burn them and exchange them for underlying reserve assets , again gaining the price differential gain. This would also bring the prices of the two markets closer together and reduce the token supply in response to a lack of demand for the token.

While these actions may be unremarkable in isolation, the systemic effects they create should be of interest to token designers. The token price chart below demonstrates this effect.

Image credit: @banteg & @Jeff Emmett

The above shows the price volatility suppression effect of PAMMs vs SAMMs in real-time token ecosystems. As mentioned above, when the token price on SAMMs exceeds the minting price on PAMMs, market participants deposit reserve assets (e.g. $ETH) into PAMMs, increase token supply, and transfer these increased tokens at a profitable price. Token sale to demand side on SAMMs. These actions not only align primary and secondary market prices, but also smooth out speculative price fluctuations that might otherwise have occurred, resulting in a more stable token price. (This is not the case for subsequent price drops, but that's a different design consideration entirely).

Essentially, the combination of PAMMs and SAMMs in a token ecosystem can have a "volatility dampening" effect on token prices. This effect has been observed both in models and in real-time deployment, although further research is needed on the limitations and potential drawbacks of these effects.

While further exploring these benefits needs to be done in follow-up articles, such as PAMMs, SAMMs, etc. have great potential to solve some key challenges in the crypto-token economy (such as reducing excessive price volatility) and deserve further research.

at last

Bonding Curves have become an integral part of the Web3 landscape and their importance will continue to grow. PAMMs and SAMMs have proven their usefulness for different scale economies. Whether it is launching an early token ecosystem or facilitating transactions in a mature ecosystem, Bonding Curve will continue to play a key role in the encryption economy in its different forms and functions.

Exploration and research on Bonding Curves is still in its early stages. Although there have been many literatures and practical applications in the field of SAMMs, PAMMs are still relatively young and understudied.