Written by | Banach
Time | 2021.02.03
Produced | NEST fans (nestfans.com) authorized by the author to publish
Many people are interested in the so-called algorithmic stablecoins, and feel that the previous collateralized stablecoins or AMMs are not new, and even fantasize that algorithmic stablecoins can accomplish what Bitcoin cannot.Mission: A fully decentralized and self-regulating global currency. The reason for this kind of idea is that apart from the inability to fully understand the blockchain and currency, the introduction of new recursive operators in algorithmic stablecoins is an important incentive:The recursive operator is relatively novel and has never appeared before, so it may make miracles vigorously.
The so-called recursive operator refers to the operator that in the continuous smart contract transformation, the next state is the operator that takes the previous state as input and repeatedly recursively generates. It is not surprising that recursive operators appear, because on the chain, the openness of data and the serial design of smart contracts constitute a time series, so that the same type of operations can be recursively processed,can lead to a non-linear structure, even a geometric progression effect. This is a very strong positive feedback feature, which is fully in line with the self-reinforcing property of the game on the chain. So for those looking for newnon-cooperative gameFor those who have no possibility, using a recursive operator is a simple and feasible solution.
Pure time series recursion is not a good idea, because the information of the next moment is completely determined by the previous moment. The ones that really deserve attention are:Combining recursive operators with others, new information is introduced in the two state changes. This information reflects the attributes of the game, so it is unpredictable. This unpredictability is also affected by the recursive operator, which has a certain common expectation, which reacts on other operators to form a resonance and produce controllable expected attributes. We call this type of operatorMultiple recursive operators.
Here is an example, taking the familiar simple algorithmic stable currency as an example, the pricing operator generates a price Pt, at this time the total expansion is a multiple recursive operator Mt, because Mt is a function of Pt, and Pt+1 It also depends on Mt, so Mt+1 and Mt establish an indirect recursive relationship, and with the cooperation of the pricing operator, a periodic negative feedback is formed, thus gradually approaching the stability of the price.This idea is based on the equilibrium of the supply and demand curve, and the game process is in the secondary market, so it is not very accurate (accurate calculation should be the functional relationship between the supply and price in the secondary market), it will As a result, the conduction process is relatively slow, and it is difficult to form a stable equilibrium.
Recursive operators can not only have operators that provide negative feedback, but also operators that provide positive feedback. This type of operator is aimed at self-reinforcing rather than algorithmic stablecoins:price stability. This typicalNEST systemIn the repurchase mechanism, repurchase leads to a decrease in market supply and an increase in price, so that the performance is better, more demand can be met, and more income can be brought, increasing repurchase, and price increase... In fact, more positive feedback can be built recursive operator,Because of its conciseness and anti-Markov properties, this method will attract more attention from developers of on-chain protocols in the future.
In a purely mathematical sense,It is unclear whether a recursive operator can build a stable short-period attribute, so it is difficult for a stablecoin built by a recursive operator to converge to a stable structure, in particular the above-mentioned,Algorithmic stablecoins do not change the direct relationship between supply and demand in the secondary market, but indirectly change the relationship between supply and demand by changing the total amount. Its conduction is slower, and there are more constraints to achieve a stable equilibrium (the possibility of instability is greater), and it is very likely Difficulty achieving your goals.
In multiple recursive operators, the step of introducing information is crucial, and the core of this step is to capture new information. To some extent, the general equilibrium property of the blockchain is indeed easy to introduce more information. This information has a certain degree of uncertainty under the design of the game structure, but this uncertainty is framed (with a unified information structure),This information is combined with the recursive operator to establish an overall expectation, which is easy to produce an illusion of stability, we think that many designs fall into this illusion. If it is not based on strict game theory analysis, it is difficult to fully grasp the overall equilibrium properties. Bitcoin just cannot become a universal currency).Sometimes in the step of information introduction, there is also a certain randomness requirement. This randomness assumes that the dependence on information is 0 (completely symmetrical), which is different from the previous stablecoin design. When this randomness and recursive operator Combining it makes it easier to produce stable traits. This kind of randomness breaks away from the structure of the game and more reflects the characteristics of the algorithm. It is the direction that algorithmic stablecoins need to mine in the future。
When we use the recursive operator,When there are too many steps to introduce information or there are too many independent operators, the effect of the recursive operator will gradually decrease, and its positive and negative feedback properties will gradually dissipate, so there is an indicator of the feedback strength of the recursive operator. If we try to strengthen positive and negative feedback when designing DeFi, we need to reduce the frequency of introducing new information. If we are pursuing a long-term regression, the introduction of information flow itself should also have certain periodic attributes, unless it can be proved that even if It is a random operator that can also achieve regression under the designed recursive operator. This design is not easy.
In the field of DeFi, most recursive operators will combine price sequences, because the price game is a game with the most concentrated information, and it is not easy to be predicted or controlled by algorithms (in fact, the price equilibrium of liquid assets is NP). However, when using the price sequence at present, it does not rely on an effective decentralized oracle, but on the AMM mechanism.This will bring predictability and controllability to the recursive operator, causing the entire recursive process to become a deterministic or controllable process, which is something that many recursive operator designers have not seriously dealt with.. This cannot simply hope that AMM will gradually become effective (fluctuation deviation is within a controllable range),Because the aggressive behavior is directly reflected in the AMM’s reserved price sequence, it cannot be automatically eliminated by the algorithm, that is, the control process cannot be eliminated by the algorithm, which will lead to the deterministic nature of the recursive operator (contrary to the uncertainty required by the recursive operator), Thus losing the meaning of design.
In addition, the recursive amount of many project designs is not directly linked to the supply and demand variable that determines the price sequence, because it is difficult to obtain this variable on the chain, but is related to the total amount of assets.This makes it impossible to go directly to the core of the game: the secondary market, the conductivity of the operator may be biased。
In the future, there should be more variables combined with recursive operators, especially the parameters that reflect the difficulty of the game in the whole market. This part is a series of nonlinear operators worthy of careful exploration, and will not be expanded here.When designing DeFi, a detailed information transmission mechanism analysis of recursive operators should be done to avoid being predicted and controlled。
