Lock Adjustments

Dynamic Locks

The lock requirement can be updated to match changes in the $ANYONE token’s value, ensuring that participation remains economically feasible and affordable for the majority of operators. Users who locked their tokens prior to such a reduction will still have the higher token amount locked. Even as the lock requirement reduces, users will still have the option to lock the maximum 100 $ANYONE tokens.

Example Adjustment: If $ANYONE is valued at $2, to encourage wider participation and to capture more relay users, the minimum stake required may be reduced to 75 $ANYONE, while still maintaining a cap at 100 $ANYONE for those who wish to maximize their involvement and potential rewards.

Overstaking Bonus

For relay fingerprints that are ‘over-staked’, with a lock value above the minimum, a modest multiplier to their relay rewards will be applied. This ensures that rewards are distributed based on the weight of both the bandwidth and the tokens staked per relay. The rewards for over-staking at a multiplier relative to the minimum stake will taper off asymptotically (at the square root).

Example: If a relay staked with 50 $ANYONE provides the same bandwidth of another relay staked with 100 $ANYONE, the second relay will receive 1.3x rewards, reflecting the relatively similar value contributed to the network's performance by each relay but accommodating a modest bonus for ecosystem stability.

Users who previously locked a higher number of tokens than the minimum are automatically enrolled into the multiplier, effectively grandfathering them into this system.

Motivation for Dynamic Staking Adjustments Based on $ANYONE Value

• Accessibility and Global Participation: To ensure that participation in the Anyone Network is economically feasible for a diverse group of operators globally, the staking requirements are dynamically adjusted based on the $ANYONE token's market value. The aim is to maintain the buy-in around $100 USD, which is considered an accessible amount for potential relay operators worldwide, irrespective of economic disparities across different regions.

• Scalability of the Network: The strategy to peg the staking requirement to a fixed USD value, rather than a fixed number of $ANYONE tokens, is designed to foster inclusivity and scalability. This approach allows the network to grow even during market fluctuations, ensuring that it does not become prohibitively expensive, thus preventing centralization of nodes while maintaining the protection offered by a lock requirement.

Justification for Overstaked Rewards and Grandfathering

• Incentivizing Long-term Commitment: Offering enhanced rewards to those who have overstaked their tokens serves as an incentive for operators to maintain or even increase their stake, contributing to network robustness. This system also discourages the unstaking of $ANYONE tokens to restake at lower prices, which could lead to increased network instability and sell pressure on the market.

• Grandfathering Existing Stakers: Operators who are currently overstaked are grandfathered into the new system with their higher stake levels intact. This policy recognizes and rewards their early and substantial commitment to the network, fostering loyalty and encouraging sustained participation.

Addendum: Mathematical Explanation of Dynamic Staking Rewards

Efficient Resource Allocation and Relay Scalability

As the value of the $ANYONE token fluctuates, our staking requirements adjust to ensure broad accessibility and optimal network participation. This dynamic adjustment means that if the $ANYONE token's value increases, the required staking amount may decrease, allowing relay operators to potentially run multiple nodes with the same total amount of staked tokens. For instance, if the token value reaches a threshold where 100 $ANYONE can support two relays instead of one, operators can double their operational nodes without additional investment, significantly enhancing network capacity and their potential earnings.

This scalability feature is designed to support a rapid expansion of network infrastructure without necessitating additional staking, simplifying the process for operators and ensuring that the network can grow to meet increasing demand efficiently.

Incentives for Overstaking and Network Stability

From a network value perspective, overstaking—staking more $ANYONE tokens than the minimum required—does not intrinsically necessitate additional rewards for the stakers. However, to encourage stability and maintain a robust relay infrastructure, the network offers modest incentives for overstaking. These incentives are not primarily about adding direct value to the network but are aimed at reducing turnover and fostering long-term commitment among relay operators.

Strategic Token Lock and Reward Distribution

The incentives for overstaking are also strategically designed to keep more tokens locked in staking contracts, which supports the overall economic stability of the network. While these overstaked tokens might offer less direct utility than those used in bandwidth authorities or other high-value roles within the network, they play a crucial role in preventing large-scale unstakings that could lead to increased volatility in the token's market value.

By keeping these tokens locked and rewarding them at a lower rate compared to more actively utilized tokens, the network can allocate more substantial rewards to areas that drive direct value, such as bandwidth provisioning and performance validation. This strategic distribution of rewards ensures that tokens are used where they can generate the most significant impact, supporting the network's long-term health and operational efficiency.

Understanding : The Reward Scaling Multiplier

In the Anyone Network, $M_{10}$ serves as a critical metric in the reward scaling mechanism, designed to ensure equitable distribution of rewards relative to the staked $ANYONE and provided bandwidth.

Definition of $M_{10}$:

• $M_{10}$: Defined as the multiplier that adjusts the rewards received by a relay when the amount of $ANYONE staked is increased tenfold, holding bandwidth constant.

Key Assumptions for $M_{10}$:

• Assumption 1: The performance and rewards of a family of 10 relays, each with identical staking and bandwidth, are considered equivalent to a single relay with ten times the staking and bandwidth when a family boost is applied. This assumption facilitates understanding how rewards scale within groups of relays operating under a unified IP.

• Assumption 2: Ten individual relays, each providing the same bandwidth and staking, collectively contribute to the network's capacity in the same way as a single relay with tenfold the resources without any family boost. This assumption supports the linear scaling of network resources and ensures that reward calculations reflect the decentralized structure of the network.

Result and Reference to Proof:

The application of $M_{10}$ within these assumptions results in a scaling factor of $M_{10}=1$, indicating that the increase in staking by ten times, under the defined conditions, does not alter the base reward multiplier, essentially making it neutral in impacting the rewards. This outcome reinforces the importance of equitable reward distribution and maintains incentive alignment across different staking levels.

For those interested in a deeper dive into the mathematical derivation and validation of $M_{10}$, please refer to the Appendix. This section of the whitepaper contains the comprehensive proof of $M_{10}$'s calculation, affirming the assumptions and their implications in the broader context of the network's economic model.