Delysium Staking

Delysium is building a framework designed to support a comprehensive Agent Network within a digital environment. By constructing mutual collaboration & communication mechanisms among several layers, Agent Network is aiming to scalable networks capable of seamlessly integrating and operating AI Agents.

By staking $AGI, all users can engage deeply with the ecosystem by receiving not only relevant rewards but also contribution certification - Loyalty Score, and other perks or privileges in the future.

AGI-USDT LP Staking

AGI-USDT v2 Liquidity Pool is now live on BNB Smart Chain PancakeSwap, all users can stake AGI-USDT LP tokens (Cake-LP) to earn $AGI.

The APR for AGI-USDT LP staking is affected by a combination of multiple factors and is subject to change at any time.

As liquidity increases, APR will decrease in relation to it. Through increasing the length of the lock-up period, the APR will increase to compensate for the time value of money. Having a higher amount of DMAs will increase the staking APR earned.

Please note that staking rewards are locked up including staking yield until the end of the period.

AGI Staking

Introduction

By simply staking $AGI through Delysium official website, all users can earn $AGI as rewards.

There are 5,000,000 $AGI in total set as rewards for all participants in this $AGI staking, with the available duration as 548 days.

All rewards will be equally issued every day during this period, which means there are around 9124 $AGI will be distributed to all staking users daily.

Users are free to choose any staking period, from a minimum of 30 days to a maximum of 365 days. Also, customizing the number of months to stake is available for all participants.

Note: When there are 30 days left until the end of the pool, it is not available to stake (the remaining time is less than the minimum staking period)

There are 2 phases for users to join AGI staking

  • Phase 1: 2 weeks after launch, it is only available to stake with the period between 6-12 months

  • Phase 2: after Phase 1 ends, it is open to all kinds of staking period

For users with specific features & historical engagement records, including DMA and Loyalty Score, they will enjoy rewards boost when staking.

  • Time boost: the longer the staking period, the higher the weight, and the more to share daily

  • DMA boost: the more DMA holding amount, the higher weight, the more to share daily

  • Loyalty Score boost: the more Loyalty Score holding amount, the higher weight, the more to share daily

After staking period is finished, the principal part will be unlocked right away while the rewards part will move into vesting phase(for each staking), which will take 60 days to fully unlock by default, and users can claim the unlocked part daily. To get a faster speed to unlock, users can stake more to get a higher vesting boost.

User Journey

Rewards Calculation & Distribution

Each user will have a User Weight

Every day, Total User Weight will be calculated among all staking users

And the % of each User Weight is

Thus, the Daily User Reward that each user can get is

What Will Affect Rewards

There are 4 factors that will affect User Weight, which will affect the how much rewards each users can get

  • AGI amount staked

  • Staking period in f(time boost)

  • DMA holding amount in f(DMA boost)

  • Loyalty Score holding amount in f(Loyalty Score boost)

f(Time Boost) = 0.5* T

T = Staking period(by month)

T ~ [1, 12]

f(DMA Boost) = 1 * sqrt(DMA amount)

DMA amount = DMA holding amount by user

f(Loyalty Score Boost) = 0.5 * sqrt(Loyalty Score/100)

Loyalty Score = Loyalty Score holding amount by user

How Will Rewards Be Vested

For each batch of rewards that are available to move into vesting phase when staking period ends, the Base speed is 1/60, which means the base vesting period is 60 days by default.

For example, if the staking period ends with a reward of 100 AGI, the daily unlocking amount without any boost is 100/60 = 1.667 AGI.

Users can staking more to get a Vesting boost, thus unlocking the total rewards faster.

For example, if a user is currently staking 100 $AGI, and the historical staking amount of $AGI is 200(including the current amount). After this staking period ends(100 $AGI), he needs to vest this part of rewards.

  • If he choose not to stake this 100 $AGI again, then the vesting boost is [1 + 0/200], which is 1, so he needs 60 days to unlock fully.

  • If he choose to stake this 100 $AGI again, then the vesting boost is [1 + 100/300], which is 1.33, so he needs 45 days to unlock fully.

  • If he choose to stake more than $100 AGI again, e.g. 500 $AGI, then the vesting boost is [1 + 500/700], which is 1.714, so he needs 35 days to unlock fully.

How To Calculate Rewards Multiplier

Since different staking periods, holding different amounts of DMA and Loyalty Score only directly affect User Weight, user rewards are dependent on the % of User Weight among all users.

Therefore, this calculation can be more intuitive to see how will be multiplier of rewards can be achieved by staking for a longer period of time, holding more DMAs and Loyalty Scores.

Theoretically, the user weight formula offers some estimation on the rewards multipliers for staking period, DMA boost and loyalty score boost. It is easy to calculate the marginal effect from each sector.

E.g. f(Time Boost), we can set it in this way - for a user, his User Weight is equal to

T is the staking period of this user, f(T) is the weight acceleration due to different staking period, and M is the sum of the other partial factors of this user's weight. And we also set the sum of the User Weights of all other users is K

Then, for this user, by choosing to stake 12 months or 1 month, the range/multiplier of Rewards changes resulting from f(T) is

And it can be turned into

By simplifying it, we can get

When the number of staking users and the number of staked AGI are large enough, the sum of all other user User Weights(K) will be much larger than the weight of that user's weight, so the right-hand side can be considered as approximating to 1. Then we can get

Similarly, we can get the marginal formula for f(DMA Boost) and f(Loyalty Score Boost)

  • For f(DMA boost)

  • For f(Loyalty Score Boost)

Based on the parameters voted by community, and the formula

  • W1 = 0.4, W2 = 0.6, W3 = 0.6, W4 = 0.4

  • f(Time Boost) = 0.5* T

  • f(DMA Boost) = 1 * sqrt(DMA amount)

  • f(Loyalty Score Boost) = 0.5 * sqrt(Loyalty Score/100)

We can calculate the specific results by involving min & max value of f(Time Boost), f(DMA boost), f(Loyalty Score Boost), then we can get

  • %(Time boost) ~ [4.125, 9.676]

    • the reward multiplier of a "12-month staking" over a "1-month staking" range from 4.125x ~ 9.676x.

  • %(DMA boost) ~ [1.213, 7.420]

    • the reward multiplier of a "holding 100 DMAs" over a "holding 1 DMA" range from 1.213x ~ 7.420x

  • %(Loyalty score boost) ~ [0.544, 6.312]

    • the reward multiplier of a "holding 35000 loyalty score" over a "holding 100 loyalty score" range from 0.544x ~ 6.312x

Note

  • Here, the maximum reward multiplier has a range instead of a fixed one, it is because each boost factor will be affected simultaneously by other two factors.

  • If a user stakes with a longer time and holds more DMA and loyalty scores compared to other users, the higher the reward multiples he can get.

Game Theory & (3,3)

The goals of vesting speed formula are

  • Encourage users to stake as more principal as possible when staking, as this will allow the user to accelerate the unlocking of rewards.

  • Encourage users to continue to stake the same amount of principal, or to stake a larger amount of principal when the staking period ends.

The mathematical principle for this formula is very simple

a/b ≤ (a+k)/(b+k)

And thus, the rational behind this mechanism is related with game theory

For any user, when one of the user's staking ends (the amount of AGI in this staking is K), assume the current total staking amount at this point is M, and the historical total staking amount is N (N includes M). The amount of AGI in the next staking is J

  • If he stakes AGI more than the amount of principal that has been unlocked (J>K), his vesting speed becomes as large as possible and he can be the first to complete the vesting, gaining a first-mover advantage. To get more AGI to stake, he needs to purchase AGI from the secondary market to complete the staking with an excess amount than current total staking amount. This behavior will bring another staking reward and increase the total yield by raising the AGI price. Thus, the benefit from this behavior can therefore be regarded as (+3)

  • If he stakes AGI equal to the amount of unlocked principal (J=K), his vesting speed will gradually become smaller and smaller, and the vesting time for him to complete the full gain is at the average level; at the same time, if he directly stakes this amount of principal again and does not go to the secondary market to purchase more AGI to participate in the staking, then he will not bring about any enhancement to the price of the AGI, and there will not be any change to his yield. Thus the benefit from this behavior can be regarded as (+1)

  • If he stakes less AGI than the amount of unlocked principal(J<K) or stakes no AGI, then the user's gain is likely to be affected by the sell-off from the accelerated vesting by the others. Thus the benefit from this behavior can be viewed as (-1)

    • In a case with 2 users, if A chooses the above strategy while B choose to stake the same or more AGI than the amount of his principal that has been unlocked, the returns of B will be potentially affected by the partial sell-off of principal by A. Thus, the benefit of B from this behavior can be regarded as (+1)

    • Similarly, if A & B both choose the above strategy, everyone's return becomes worse, so the benefit of both A and B from this behavior can be regarded as (-3)

Thus, we have such conclusions

  1. when every user stakes more AGI and continues to stake excess principal after the staking period ends, all users' return becomes better

  2. when a user stakes more AGI with a sufficiently large amount of excess principal, his return is the highest of all users

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