Desirable Price Function and Value Ratio of Constant Function Market Makers

Decentralized exchange was a revolution in cryptocurrency trading. Decentralized exchange presented a method to set prices mathematically without an order book. Order books have been a widely-known method of determining prices for over 400 years. Decentralized exchanges devised a constant function market maker to mathematically determine prices. Among them, constant product market makers are the most widely used. In addition, several constant function market makers have been proposed. However, there was no discussion about the desirable requirements of a constant-function market maker. In this paper, we discuss the desirable requirements of a constant function market maker and show that the constant product market maker is still the most desirable constant function market maker.