In-depth Thinking on DEX Trading Operator Design

When developing the decentralized exchange (DEX), designing trading operators is a core task. Trading operators can be linear or nonlinear, and this choice will have a profound impact on the operation of the DEX.

The linear trading operator is based on the theory of equilibrium price, assuming that there are no arbitrage opportunities in the market. In a complete market, only linear trading operators can guarantee no arbitrage. However, linear operators are difficult to realize protocol value capture and tokenization, as they are equivalent in any contract and cannot form unique advantages.

Non-linear trading operators attempt to simultaneously achieve pricing, trading, and value preservation. They can be designed with scale-related self-reinforcing properties to capture value. However, this approach also faces many challenges: in complete markets, they can only fit linear operators within a very small range; in incomplete markets, efficiency and costs are questionable; and the sources of value inputs are unclear and may be lost.

Currently, many AMMs use a fixed product model ( such as XY=K), which is a typical scale-related nonlinear operator. It can only simulate linear trading locally when the liquidity pool is large enough. In contrast, some oracle-based linear models may be more intrinsic and natural.

Putting pricing power entirely on-chain may be a misunderstanding. The discreteness and auction characteristics of on-chain transactions make it difficult to meet the demand for effective pricing in a complete market. For incomplete markets (, such as new projects ), the key lies in quickly and cost-effectively forming prices and completing a large number of transactions, rather than preventing arbitrage.

Non-linear operators perform pricing and trading simultaneously, but are at a disadvantage in trading efficiency compared to oracle models. Their advantages may only exist in terms of pricing costs and efficiency, but this still requires further research.

Value input is another challenge faced by nonlinear operators. In a complete market, a large number of small transactions are needed to compensate for arbitrage losses, but this may become difficult to achieve due to increased on-chain costs. In a highly incomplete market, any nonlinear operator can meet trading demands, with a focus on maximizing trading volume.

In summary, nonlinear trading operators are not an ideal choice for capturing value in decentralized protocols. In contrast, interest rate operators have certain value due to the higher difficulty of arbitrage, but this is more of a stopgap measure rather than an essential innovation.

Future improvements may lie in the introduction of recursive information, utilizing historical transaction data to reduce arbitrage risks. This requires an in-depth analysis of the core risks behind the operators and a clear definition of trading objectives. Unifying financial services under operator theory and developing more effective mathematical models is key to promoting the development of on-chain finance.