Paradigm's latest research: understanding progressive Dutch auction

Foresight News 2022-04-06 13:11:50 阅读数:891

paradigm latest research understanding progressive

writing :Frankie、Dan Robinson、Dave White

compile :Amber

This paper introduces the progressive Dutch auction (Gradual Dutch Auction, Hereinafter referred to as GDA), An auction mechanism that can effectively help illiquid assets complete public sales .

GDA With the previously proposed 「 Time weighted average market maker (TWAMM)」 The mechanism is intended to solve problems similar to , It can make assets circulate and sell effectively on the basis of not relying on the existing liquidity of the market .

GDA The working principle of is to decompose an auction into a series of Dutch auctions ( notes : Dutch auction is a common form of auction , Will start with a high asking price , Then gradually reduce , Until the buyer bids ).GDA Allows you to conveniently participate in multiple such auctions at the same time .

This article will provide information more suitable for NFT Discontinuous type of sales GDA And more suitable for token auction GDA Two models , For readers to understand this new auction mechanism .

Discontinuous type GDA

hypothesis Alice Want to sell 1 Thousands of pieces of NFT. She's not sure about these NFT Fair value of , So she doesn't want to sell at a fixed price .

contrary , She may choose to hold a Dutch auction —— Start with a high asking price , Then gradually reduce the price , Until all NFT All sold . However, this method is not necessarily the optimal solution , Because buyers in the market may not be able to digest all at once NFT works .

contrary , If Alice One auction at a time NFT. for example , She may start a new Dutch auction every minute , Auction a new work of hers . This will give the market more time for her NFT Find a fair price for art .

Discontinuous type GDA In fact, it is an extension of this idea .


Discontinuous type GDA Applicable to sales NFT, Because these assets must be sold in whole numbers . The working principle is for each NFT Hold a virtual Dutch auction . In a discontinuous GDA in , Every auction starts at the same time , Each virtual independent auction has a higher starting price . The price of each auction is given by the price function , The parameters of the function include the ranking of the auction in the series of auctions , And the time since the beginning of the normal auction .

A better function obtained through calculation is as follows :


among , The price of each auction is based on the attenuation constant λ Decays exponentially , The starting price of each auction is increased by a fixed proportional factor α, The starting price of the first auction is from the initial price k decision .

Price calculation of batch auction

According to the above price function , We can calculate the total price of the batch auction .

Assume Bob The quantity you want to buy is q Assets to be auctioned . To do this , He will buy a total of... In each independent Dutch auction q The cheapest asset . The current time is after the auction starts T moment , The total amount sold so far is m, be Bob Buy q The total price of the quantity asset P by :


After substituting the price function , We can get the final price calculation formula :


If you assume some specific values , We can get the following result case :


Continuous type GDA

At the completion of NFT After sale ,Alice Now I want to sell some standard tokens . Of course, she can also use the above discontinuous type GDA Mechanism , pack 「 piecewise 」 Sell her tokens .

However Alice Maybe she doesn't want all her tokens to be sold immediately , For example, she wants the token to be on a daily basis 360 Release at a constant speed . Then she can choose to sell her tokens in a series of standard Dutch auctions , Instead of using it once GDA Make all sales . For example, she can do it every hour 15 Token auction , Or every minute 0.25 Token auction, etc .

Continuous type GDA The working principle of is to limit the process to the limit , That is, the time interval between auctions is close to 0. This means that the sale is divided into an infinite sequence of auctions , Each auction sells an unlimited number of tokens .


The continuous working principle is to gradually provide more assets available for sale at a constant emission rate . The whole auction process will be broken down in a series of virtual auctions . These auctions over time , Start at a uniform speed , Every auction starts at the same price .

The price of each auction is given by a price function , Since the beginning of the auction . Price model and discontinuous model GDA similar , The price depends on the attenuation constant λ Decays exponentially , At the same time, the starting price of the auction is k:


The price of participating in the auction is calculated

If Bob The quantity you want to buy is q Token of , In order to buy the corresponding number of tokens , He needs to be involved q/T The auction , Because the price of the auction continues to decline , So he needs to quote for the first of all the current independent virtual auctions that can be quoted .

Suppose the duration of the earliest auction is T, So the quantity q The total price of tokens P by :


Without considering the interaction cost on the chain , After substituting the price calculation formula , The complete price formula is :


After substituting some assumed parameters , The following example results can be obtained :



Paradigm And publicly shared GDA Model Python Model as well as Feasibility test .


GDA It can be used for the public sale of homogeneous or non-homogeneous assets , And it is more valuable for assets that lack basic liquidity , The use scenario of this auction mechanism is not limited to the simple cases mentioned in this article , It is expected to land in more application scenarios in the future .

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