Restaking Incentives
Introduction
In addition to staking rewards, the Tangle Network offers a restaking system designed to encourage operators to execute Actively Validated Services (AVS) instances. This documentation provides an overview of the restaking process, reward mechanisms, and the benefits for operators and delegators participating in the Tangle blockchain network.
Eligibility
 operators on the Tangle blockchain can establish a restaking profile by allocating 50% of their locked and nominated stake towards restaking.
 delegators associated with these operators receive proportional rewards, enhancing the benefits of participating in the restaking system.
Reward Subtypes
The rewards for restakers adjust proportionally based on several factors, including the amount of tokens restaked, the number of jobs completed, and the diversity of roles engaged in restaking.
The reward distribution mechanism for restakers is bifurcated into two segments:
Active Participation Rewards
The main form of reward is the income from providing services. These are fees users pay to have restaked operators perform MPC and ZK services. Rewards are based on the validator's participation in and completion of total job opportunities, benefiting the most active and reliable restakers.
 The total jobs completed (TJC) by all active operators are calculated.
 Each validator's share (VS) of the rewards is determined by the proportion of their completed jobs relative to the TJC.
 The validator reward (VR) is computed as: VR = VS × Total Rewards
Continuous Restaking Rewards:
In addition, To motivate operators to opt into MPC service roles, Tangle rewards them with additional inflationary rewards on top of their standard validation rewards, merely for restaking their tokens.Rewards are allocated in proportion to the overall restaking distribution, maintaining the incentive for continuous restaking. The reward rate for this is programatically limited to a range of 0.1% and 2%, in a similar style to the core staking rewards system of Substrate blockchains.
 The total restake (TR) in the system is calculated by summing all operators' restaked amounts.
 The restaketostake ratio (RSR) is computed as: RSR = TR / Total Stake in the Era
 The missing restake ratio (MRR) is calculated as: MRR = Maximum Restake Ratio  RSR
 The adjusted total rewards (ATR) are computed based on the MRR to ensure proper reward distribution.
 Each validator's reward share (RS) is determined by their restaked amount relative to the TR.
 The final reward for each validator is calculated as: Reward = RS × ATR
Additionally, a decay rate ($d$) is used to reduce the rewards rate when restaking participation exceeds the ideal target of 25% of TNT.
Example Reward Calculation
Let's consider an example in era 100, with 20 restakers and a total role reward of 1000 TNT:

Active Validator Rewards:
 10 restakers have completed 5 jobs each.
 50% of the 1000 TNT (500 TNT) is equally divided among the 10 active restakers.
 If one restaker had completed more jobs than the others, they would receive a larger share of the rewards.

Rewards by Restake:
 The remaining 50% of the 1000 TNT (500 TNT) is distributed among all restakers based on their restaked amount.
 If a restaker has restaked 100 TNT out of a total restake of 1000 TNT, they are eligible for 10% of the rewards.
 The rewards are adjusted based on the total restake relative to the total stake in the system.
Calculation Logic for Restaking Reward
Rewards and the Restaking Profile
To begin restaking, a validator must create a restaking profile. A restaking profile involves allocating a portion of the validator's staked tokens to specific roles. There are two types of restaking profiles:
Independent Restaking Profile: The restake amounts are allocated independently to each selected role, such that:
$\sum_{r \in p} \text{role\_restake}(p, r) = \text{total\_restake}(p)$
Shared Restaking Profile: The restake amounts are allocated collectively to all selected roles, such that:
$\text{role\_restake}(p, r) = \text{total\_restake}(p)$
A validator can update their restaking profile to switch between profile types, adjust the restake amounts allocated to various roles, or add/remove roles from their profile. The specific constraints for updating a restaking profile depend on whether the profile is active or not.
Active Participation Restaking Rewards
Restaking rewards are calculated based on the validator's participation in various roles and their restaking fraction.
The reward function for a validator $v$ over a time interval $T$ is defined as:
$R(v, T) = \texttt{payout}(T) \times \left(\sum_{r} \alpha_r \times \texttt{dist}(v, r, T) + \left(1  \sum_{r} \alpha_r\right) \times f_{\texttt{restake}}(v)\right)$
where:
Expression  Description 

$\texttt{payout}(T)$  The total amount of tokens to be distributed as restaking rewards over the time interval $T$. 
$\alpha_r$  The weight assigned to role $r$ in the reward distribution ($\sum_{r} \alpha_r \leq 1$). 
$\texttt{dist}(v, r, T)$  The fraction of jobs with role $r$ completed by validator $v$ over the time interval $T$. 
$f_\texttt{restake}(v)$  The fraction of total restake by validator $v$. 
The total payout for a given time interval $T$ is calculated as:
$\texttt{payout}(T) = I_{\texttt{NPoS}}(x) \times \texttt{total\_supply}$
where:
Expression  Description 

$I_{\texttt{NPoS}}(x)$  The annual inflation rate for restaking rewards, which depends on the current staking rate $x$. 
$\text{total\_supply}$  The total token supply (100 million TNT). 
Continous Restaking Rewards (Annual Restaking Inflation Rate)
The annual inflation rate for restaking rewards is dynamic and designed to incentivize a target staking rate of 25% of the total token supply. The inflation rate is calculated using the following piecewise function:
$I_\texttt{NPoS}(x) = \begin{cases} I_0 + (I_\texttt{ideal}  I_0) \times \frac{x}{\chi_\texttt{ideal}}, & \text{for } 0 < x \leq \chi_\texttt{ideal} \ I_0 + (I_\texttt{ideal}  I_0) \times 2^{(\chi_\texttt{ideal}  x) / d}, & \text{for } \chi_\texttt{ideal} < x \leq 1 \end{cases}$
where:
Expression  Description 

$x$  The staking rate (ratio of the total amount of tokens staked to the total token supply) 
$\chi_{\text{ideal}}$  The ideal staking rate (25% or 0.25) 
$I_0$  The minimum inflation rate when the staking rate is close to zero (0.1% or 0.001) 
$I_{\text{ideal}}$  The maximum inflation rate when the staking rate equals the ideal staking rate (2% or 0.02) 
$d$  The decay rate, which determines how quickly the inflation rate decreases when the staking rate exceeds the ideal rate (suggested value: 0.05) 
Calculating Total Restaking Rewards: Combined participation and continuous restaking
To estimate a validator's restaking rewards, the following inputs are required:
 The validator's restaking profile (independent or shared)
 The total amount of tokens restaked by the validator $\texttt{total\_restake}$
 The amount of tokens restaked by the validator for each role $r$ $\texttt{role\_restake}(r)$
 The fraction of jobs with each role $r$ completed by the validator $\texttt{dist}(v, r, T)$
 The total token supply $\texttt{total\_supply}$
 The current staking rate $x$
 The weights assigned to each role $r$ $\alpha_r$
With these inputs, the restaking rewards can be calculated using the following steps:

Calculate the annual inflation rate for restaking rewards $I_\texttt{NPoS}(x)$ using the piecewise function based on the current staking rate ($x$)

Calculate the total payout for the time interval $T$ $\texttt{payout}(T)$ using the formula:
$I_\texttt{NPoS}(x) \times \texttt{total\_supply}$
 Calculate the validator's restaking reward $R(v, T)$ using the reward function:
$R(v, T) = \texttt{payout}(T) \times \left(\sum_{r} \alpha_r \times \texttt{dist}(v, r, T) + \left(1  \sum_{r} \alpha_r\right) \times f_\texttt{restake}(v)\right)$