Paradigm: Explaining Progressive Dutch Auctions
Original title:Gradual Dutch Auctions
Author: Frankie, Dan Robinson, Dave White
Original compilation: Amber, Foresight News
Original compilation: Amber, Foresight News
This paper introduces the Gradual Dutch Auction (GDA), an auction mechanism that can effectively help illiquid assets complete public sales.
GDA is similar to the problem that the "Time Weighted Average Market Maker (TWAMM)" mechanism that has been proposed before aims to solve. It allows assets to be effectively circulated and sold without relying on the existing liquidity in the market.
GDA works by breaking down an auction into a series of Dutch auctions (note: a Dutch auction is a common auction format that starts with a high asking price and gradually lowers it until a buyer bids). GDA allows you to participate in multiple such auctions at the same time in a convenient way.
This article will provide two models of discontinuous GDA more suitable for NFT sales and continuous GDA more suitable for token auctions for readers to understand this new auction mechanism.
Discontinuous GDA
Suppose Alice wants to sell 10,000 NFTs. She's not sure of a fair price for these NFTs, so she doesn't want to sell them at a fixed price.
Discontinuous GDA is actually an extension of this idea.
Discontinuous GDA is actually an extension of this idea.
mechanism
mechanism
Discontinuous GDA is suitable for selling NFTs because these assets must be sold in whole numbers. It works by holding a virtual Dutch auction for each NFT. In a non-sequential GDA, each auction starts at the same time, and each virtual independent auction has a higher starting price. The price of each auction is given by the price function whose parameters contain the order of the auction in the series, the time since the start of the normal auction, etc.
A better function obtained through calculation is as follows:
Among them, the price of each auction decays exponentially according to the decay constant λ, the starting price of each auction is increased by a fixed proportional factor α, and the starting price of the first auction is determined by the initial price k.
Price Calculation for Lot Auctions
Based on the above price function, we can calculate the total price of the lot auction.
Suppose Bob wants to buy an amount of q assets to be auctioned. To do this, he buys the cheapest asset for a total of q in each independent Dutch auction. The current time is T after the start of the auction, and the total amount sold so far is m, so the total price P for Bob to purchase q amount of assets is:
After substituting the price function, we can get the final price calculation formula:
If we assume some specific values, we can get the following result case:
Continuous GDA
After completing the NFT sale, Alice now wants to sell some standard tokens. Of course, she can also use the above-mentioned non-continuous GDA mechanism to package and sell the tokens in her hands in "segments".
The working principle of continuous GDA is to limit this process to the limit, that is, the time interval between auctions is close to zero. This means that the sale is divided into an infinite sequence of auctions, each auction selling an infinitely small number of tokens.
mechanism
mechanism
Ongoing works by gradually making more assets available for sale at a constant emission rate. The entire auction process is broken down in a series of virtual auctions. These auctions start at an even pace over time, with each auction starting at the same price.
The price of each auction is given by some price function, where is the time since the auction started. The price model is similar to the discontinuous GDA, the price decays exponentially according to the decay constant λ, and the starting price of the auction is k:
Price Calculation for Participation in Auctions
If Bob wants to buy a quantity of q tokens, he needs to participate in q/T auctions in order to purchase the corresponding quantity of tokens. The first ones in the auction to start make bids.
Assuming that the duration of the earliest auction started so far is T, then the total price P for the quantity q of tokens is:
After substituting some assumed parameters, the following sample results can be obtained:
the code
the codePython modelas well asFeasibility test。
in conclusion
in conclusion
