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How does Perpetual Protocol use zero-sum game principles to change AMM?

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Perpetual Protocol seems to adopt common AMM mechanisms, but the fundamentals are completely different from those of a spot AMM trading platform. To fully understand vAMM's operation mechanism, it is necessary to begin by understanding the fundamental dif

With the gradual implementation of Layer 2 and other expansion schemes, the projects in the derivatives track have recently attracted people's attention again, and the token prices of some head projects have also recently hit a record high. This includes the Perpetual Protocol, which has long occupied the number one trading volume in the Perpetual contract segment.

In the previous article,Why are perpetual contracts the most promising area of derivatives?", the Research Institute has discussed the reasons why perpetual contracts are more suitable for the on-chain trading environment than delivery contracts. In this paper, we will focus on analyzing the core trading mechanism of the current version V1 of Perpetual Protocol, and introduce in detail the fundamental differences between the derivative market and the spot market, as well as the innovations of Perpetual Protocol's original virtual Automated Market Maker (vAMM) mechanism.

VAMM is not really AMM

The traditional AMM trading model has had a large number of successful cases in the spot market. However, no matter how special its market-making function is, the basic structure of each AMM platform can be no more than two parts, that is, the quotation algorithm and the liquidity in the capital pool. Therefore, the formula can be expressed as:

AMM Trading Platform = AMM Automatic quotation algorithm + Liquidity Provider (LP)

Among them, the AMM automatic quotation algorithm has a number of mature solutions to choose from, such as the Perpetual Protocol team adopted the x*y = K constant product model. But for many nascent DeFi protocols, the more critical issue is often how to obtain sufficient liquidity support in the early stages of development.

Unlike other projects that purchase liquidity through an incentive mechanism, the Perpetual Protocol team chose to actively circumvent the problem of access to liquidity during research and development and developed a unique virtual automated market maker mechanism known as vAMM. The main reason it is called virtual AMM is that its structure no longer includes the role of liquidity provider.

Therefore, the above formula can be modified as follows:

VAMM trading platform = AMM automatic quotation algorithm

After these bold changes, the vAMM platform's only function is to provide traders with instant quotes. Therefore, it can be said that the Perpetual Protocol V1 version based on the vAMM mechanism is not a traditional AMM trading platform, and there is no real liquidity in the platform, and the role of liquidity provider. Naturally, no LP has to take risks like volatile losses.

Of course, for traders, whether there is a liquidity provider behind the platform has no effect at all, and the trading experience is no different from that of ordinary AMM. The following is a screenshot of the ETH/USDC transaction pair on Perpetual Protocol making transactions. The components, in order, are:

1. Access margin button: Only after a certain amount of margin has been pledged, you are eligible to start trading;

2. The choice of trading long and short direction;

3. The number of transactions and the amount of margin occupied

4. Leverage multiple (currently, the maximum leverage is 10 times open)

5. The maximum slip a trader is willing to tolerate;

As you can see, the experience of trading on Perpetual Protocol is essentially the same as that of Trading on Uniswap, with the exception of increased margin access and trading leverage multiple options. This is the biggest advantage of Perpetual Protocol, which enables users to have a similar trading experience to the spot trading platform without the need for LP.

However, if there is no real money to make the market on a trading platform, then who are the traders on the platform buying assets from and selling them to?

To understand this, we need to understand the fundamental difference between the derivatives market and the spot market.

The fundamental character of the derivatives market is a zero-sum game

Most readers have probably heard of the concept of zero-sum games, but why some markets are zero-sum and others are not is a question that many readers probably haven't given much thought to.

The derivatives market in reality is a typical zero-sum game market. Let's take a futures exchange in traditional finance as an example. When you choose to go long or short, you have to find a counterparty to go against you. Therefore, in the traditional futures market, each transaction will generate or destroy a multiple order and a short order at the same time, or transfer an existing multiple order or short order, so that the futures market will always maintain the same number of multiple order and short order.

So any gains on either side must correspond to losses on the other side of the market by the same amount. This makes the futures market become a zero-sum game market, in which all participants can only enter the game by paying margin, and eventually settle profits and losses through margin, and the profits can only be reflected in the increase or decrease of margin balance.

This zero-sum game does not increase the overall wealth of society, but it does have the other advantage that the game no longer requires real assets. The liquidity needed in a traditional derivatives market, therefore, does not require real assets, but a market with enough players that it is easy for any of the players to find counterparties in the opposite direction.

How does Perpetual Protocol construct zero-sum game markets

Perpetual Protocol's game mechanics are similar, but with a few differences.

When a player in Perpetual Protocol opens multiple or empty orders, it no longer needs a counterparty in the opposite direction of the game to exist simultaneously, but directly makes settlement with the vAMM algorithm. In order to maintain the multi-empty identity, it is necessary to introduce a new dimension, namely time.

As traders in Perpetual Protocol need to liquidate their positions regardless of their eventual profits or losses (liquidating is the reverse of the initial opening), in the vAMM trading market of Perpetual Protocol, All long and short orders maintain a long and short identity in time. Before any participant leaves the vAMM platform, the number of multiple orders submitted is identical to the number of empty orders.

This feature gives Perpetual Protocol many advantages that are not available on other trading platforms. There is no need to incentivize liquidity, no need to worry about the volatility of LP losses, no need to create new markets according to demand, etc.

However, while enjoying these advantages, there is still a problem of vAMM mechanism that is not solved, that is, the setting of k value in x*y=k.

How is the value of K determined in vAMM

In a normal AMM trading platform, the size of the K value requires no human intervention at all, as its size depends only on the amount of real liquidity in the capital pool. However, in vAMM trading platform, since there is no real liquidity, the value of K in x*y= K becomes a problem requiring managers' subjective judgment.

In the scheme adopted by Perpetual Protocol V1, the k value is actively managed by the project team. However, it is a careful balancing task to set the value of K artificially. If the value of K is set too high, the virtual liquidity in vAMM will be too high, and the impact of a transaction on the existing price will be small. This naturally reduces the slippage that users incur during trading, but if there are too few traders in a virtual pool and the target price moves too quickly, it is easy to break the anchor between the contract price and the target price, undermining the product structure of perpetual contracts. If the value of K is set too low, traders in the virtual capital pool will suffer a higher trading slip point, which will lead to a decline in traders' experience.

This kind of setting work, whether completed by centralized team or decided by community governance vote, has certain defects in efficiency and fairness. Therefore, how to change the setting of k value to be performed by market or algorithm as soon as possible has become an urgent problem to be solved by Perpetual Protocol.

In the current version, the k value is set to artificially reference the real liquidity of the same trade in Uniswap. The real market is used as a reference to reduce the adverse impact of subjective judgment. The development team at Perpetual Protocol has also attempted to develop automated algorithms for "floating K values". However, after the team weighed the pros and cons, the "floating K value" scheme was finally abandoned in the V2 version upgrade.

In the next article, we will highlight the new transaction engine used by Perpetual Protocol V2 and its key improvements in capital efficiency and platform openness. Moreover, by comparing the development trajectory of spot trading platform, we analyze whether it is possible to continue to grow into the leading project of the perpetual contract trading track.