---
# System prepended metadata

title: veTokenomics for Pods
tags: [reppo]

---

---
title: veTokenomics for Pods
tags: reppo
---

# veTokenomics for Pods

## Overview

Reppo is a network of composable intelligence.  In the Reppo network, "Pods" are units of intelligence. The rationale behind using veTokenomics for Pod tokenomics is that it is an effective and proven way to incentive align network participants.  

In brief, the Reppo veTokenomics model works as follows. Users can stake Reppo tokens for veReppo tokens. Users allocate veReppo tokens to different pods. This does the following: a) Enables the user who staked into a Pod to receive a pro-rata proportion of fees that the Pod generates, and b) Redirects a portion of the total Reppo token emissions to that Pod. 

Why does this make sense for the Reppo network? Pods are like businesses (in Reppo's case, they are businesses that specialize in producing a specific kind of intelligence). Businesses may need startup capital and look for investors to get this seed money, and in exchange they trade their equity, which is effectively a bet on the future cash-flow of that company. The mechanism in this document tries to achieve this exact dynamic, in a tokenized manner.

In this document, we describe an updated version of the veTokenomics model that better aligns with the vision of the Reppo network.  The key updates to the original veTokenomics model are:

**Non-Linear veToken Issuance**: Longer lock periods yield higher veToken allocations, incentivizing long-term commitment.

**Startup-Style Investment Claims (FCUs)**: Allocating veTokens to a pod grants Fee Claim Units (FCUs), giving holders rights to a share of future earnings.

**Adjustable Fee Splits**: Pods configure how much of their fees go to stakers vs. how much they retain - enabling them to develop their own strategies that attract capital (e.g. high fee sharing) or fund internal growth (e.g. low fee sharing).

**Gradual Emission Ramp-Up**: New pods start with reduced emissions and must reach or exceed median fee performance to unlock full emission benefits. This is a protection mechanism to prevent reward farming.

**Diversity Incentives for Vote Allocation**: To encourage discovery of new Pods and foster their development, voters who diversify their investments receive a boost, while pods dominating too much vote share face diminishing returns.

**Early Unstaking Penalties**: Early unlocks incur penalties and forfeiture of FCUs, discouraging short-term speculation and reinforcing long-term participation.

Overall, this integrated veTokenomics framework aligns incentives across all stakeholders:  
- **Long-term stakers** are rewarded with greater governance power, sustained fee claims, and higher potential returns.  
- **Pod operators** gain the freedom to fine-tune their offerings, balancing immediate payouts to attract stakers with the need to retain capital.  
- **The network as a whole** benefits from a robust, decentralized, and performance-driven marketplace of pods, ensuring ongoing innovation, fair resource distribution, and resilient growth.

---

### 1. Non-Linear veToken Issuance

**Mechanism:**
- Users lock Reppo tokens for a chosen duration.
- The veToken amount increases non-linearly with the lock length, rewarding larger allocations to users who commit for longer periods.
  
**Rationale:**
- Incentivizes long-term commitment and stability.
- Aligns veToken holders more closely with the long-term health and success of the network.

---

### 2. Reduce Pod Onboarding Friction

**Mechanism:**
- Pods pay a registration fee to join.
- There are no strict upfront performance requirements; pods start with reduced emission benefits and must earn full benefits by demonstrating performance over time.
  
**Rationale:**
- Encourages innovation and easy market entry.
- Pods must prove themselves through performance to unlock full rewards.

---

### 3. Gradual Emission Ramp-Up

**Mechanism:**
- Each epoch, the median fee generation across pods is calculated.
- New pods begin at a low emission multiplier and progressively earn a higher multiplier as they match or surpass the median fees for consecutive epochs.
- After meeting these performance benchmarks, pods receive full emission benefits.

**Rationale:**
- Ensures emissions are funneled towards pods that deliver real value.
- NOTE: we can update the exact mechanics of this as desired.

---

### 4. Diversity Incentives for veToken Voting

**User-Level Vote Distribution Bonus:**
- Distributing votes across multiple pods increases a user’s effective voting power. 

**Pod-Level Concentration Penalties:**
- If a pod accumulates a large share of total veToken votes, diminishing returns are applied on emissions beyond a threshold encourage voters to diversify.

**Rationale:**
- Prevents ecosystem stagnation and dominance by a few pods.
- Encourages a tradeoff between exploration and exploitation to avoid local minima in pod investments.

---

### 5. Startup-Style Investment Claims on Future Fees (FCUs)

**Mechanism:**
- veToken voters receive Fee Claim Units (FCUs) tied to their chosen pods, which can potentially be issued as NFTs and are tradeable.
- FCUs represent a claim on the pod’s future fees for a specified vesting window.
- As long as voters maintain their allocation, they continue earning new FCUs. If they reallocate votes away, they stop accruing new FCUs but retain existing units.  
- FCUs do not expire and, therefore, model shares in a company.

**Rationale:**
- Mimics equity-like claims, giving early supporters long-term upside.

---

### 6. Adjustable Fee Splits for Pods

**Mechanism:**
- Each pod sets a “Fee Split Parameter” determining what percentage of fees go to stakers versus how much the pod retains.
- Pods can adjust this parameter over time.

**Rationale:**
- Enables flexibility for pod strategy.

---

### 7. Penalties for Early Unstaking

**Mechanism:**
- Early unstaking is allowed but penalized.
- The penalty grows non-linearly the earlier a user attempts to unstake relative to their chosen lock duration.
- All unvested FCUs and unclaimed emissions are forfeited upon early exit.

**Rationale:**
- Discourages short-term behavior.
- Simultaneously, enables withdrawal of stake in emergency scenarios thereby keeping things as liquid as possible.

---

# Mathematical Specification

In this section, we describe a mathematical formulation of the above described veTokenomics.

## Definitions
- $E$ - an Epoch
- $R_E$: Total new tokens minted by the protocol in epoch $E$ for distribution as emissions.
- $\text{regFee}$: Registration fee for creating a new pod.
- $L_{\max}$: Maximum lock duration allowed for users.
<!-- - $C$: A constant used in the user-level vote distribution bonus formula. -->
- $\theta$: Threshold fraction of total votes for triggering concentration penalties.
- $\omega$: FCU accrual rate
- $\tau$: FCU vesting window (in epochs), determining how long FCUs last.
- $\gamma > 1$: A parameter controlling the non-linearity of veToken issuance.

## User Locking and veToken Issuance

For each user $u$:

- $X_u$: Amount of base tokens the user locks.
- $L_u$: User’s chosen lock duration (in epochs).
- $t_u$: The number of epochs elapsed since the user’s lock began.
- $r_u = \frac{t_u}{L_u}$: Fraction of the lock period completed.

$$
V_u = X_u \left(\frac{L_u}{L_{\max}}\right)^\gamma.
$$

If $\gamma > 1$, longer lock durations yield disproportionately more veTokens.

## Early Unstaking Penalties

Define the penalty to be applied to unstaking as:
$$
\text{Penalty}(u) = X_u \cdot (1 - r_u)^2.
$$

- The user receives $X_u - \text{Penalty}(u)$ base tokens back.
- The user forfeits all unvested FCUs and any unclaimed emissions.
- Note that if $r_u = 1$, then there is no unstaking penalty.

## Pods

For each pod $p$:

- Pods pay $\text{regFee}$ at creation.
- $FEE_{p,E}$: Fees generated by pod $p$ during epoch $E$.
- $\alpha_p \in [0,1]$: Fee split parameter. Fraction of fees distributed to FCU holders; the remainder $(1-\alpha_p)$ is retained by the pod.
- Pods start with reduced emissions until they meet performance criteria.

## Votes

At the start of each epoch $E$:

- Users allocate their veTokens $V_u$ across pods.
- Let $v_{u,p,E}$ be the veVotens allocated by user $u$ to pod $p$ in epoch $E$.

Total votes for pod $p$:

$$
V_{p,E} = \sum_{u \in U} v_{u,p,E}.
$$

Total votes overall:

$$
V_{E}^{total} = \sum_{p \in \mathcal{P}} V_{p,E}.
$$

## Diversity Incentives

### User-Level Vote Distribution Bonus

Let $N_{u,E}$ = number of distinct pods that user $u$ votes for in epoch $E$.

Effective total votes for user $u$:

$$
V_{u,E}^{eff,total} = \left(\sum_{p \in \mathcal{P}} v_{u,p,E}\right) \left(1 + \frac{\log(N_{u,E})}{C}\right).
$$

Rescale each $v_{u,p,E}$ proportionally:

$$
v_{u,p,E}^{\prime} = v_{u,p,E} \cdot \frac{V_{u,E}^{eff,total}}{\sum_{p \in \mathcal{P}} v_{u,p,E}}.
$$

The effective votes for pod $p$ are:
$V_{p,E}^{eff} = v_{u,p,E}^{\prime}$

$C$ is a constant to be decided.

## Performance-Based Emission Ramp-Up

Compute the median fee generated in an Epoch:

$$
M_E = \text{median}(\{FEE_{p,E} : p \in \mathcal{P}\}).
$$

Define the emission multiplier $\mu_{p,E}$ for pod $p$:

$$
\mu_{p,E} = 
\begin{cases}
0.25 & \text{if } FEE_{p,E} < M_E \\
0.50 & \text{if } FEE_{p,E} \geq M_E \text{ for 1 consecutive epoch} \\
0.75 & \text{if } FEE_{p,E} \geq M_E \text{ for 2 consecutive epochs} \\
1.00 & \text{if } FEE_{p,E} \geq M_E \text{ for 3 consecutive epochs (pod graduates)}
\end{cases}
$$

Once graduated, $\mu_{p,E} = 1.00$ thereafter.

## Emission Distribution

Total emissions $R_E$ per epoch are distributed to pods proportionally:

$$
\text{Emission}_{p,E} = R_E \cdot \frac{V_{p,E}^{eff} \cdot \mu_{p,E}}{\sum_{p' \in \mathcal{P}} (V_{p',E}^{eff} \cdot \mu_{p',E})}.
$$

User’s share of pod $p$ emissions in epoch $E$:

$$
\text{EmissionShare}_{u,p,E} = \text{Emission}_{p,E} \cdot \frac{v_{u,p,E}^{\prime}}{\sum_{u'} v_{u',p,E}^{\prime}}.
$$

## Future Claim Units (FCUs) with Pod-Specific Payout Delay

Each pod $p$ chooses a parameter $\delta_p \geq 0$ that determines how long after FCU acquisition the payout window begins. Thus, FCUs represent a forward-looking claim on the pod’s fees, starting $\delta_p+1$ epochs after acquisition and continuing for $\tau$ epochs.

### FCU Acquisition

At the end of each epoch $E'$:

- Users earn FCUs based on their effective votes $v_{u,p,E'}^{\prime}$:
  
  $$
  \Delta \text{FCU}_{u,p,E'} = v_{u,p,E'}^{\prime} \cdot \omega.
  $$
  
- These FCUs are associated with the acquisition epoch $E'$:

  $$
  \text{FCU}_{u,p,E'}^{(acq)} = \Delta \text{FCU}_{u,p,E'}.
  $$

$\text{FCU}_{u,p,E'}^{(acq)}$ denotes the batch of FCUs earned by user $u$ for pod $p$ at the end of epoch $E'$.

---

### FCU Activation and Duration

For a given pod $p$:

- FCUs acquired at epoch $E'$ become active starting at epoch $E' + \delta_p + 1$.
- Once active, they remain active for $\tau$ consecutive epochs.

Thus, the FCUs acquired at epoch $E'$ pay out from epoch $E' + \delta_p + 1$ through epoch $E' + \delta_p + \tau$.

---

### Determining Active FCUs at Epoch $E$

At epoch $E$, to find the FCUs currently paying out, consider the acquisition epochs $E'$ for which the FCUs are active. FCUs start paying out $\delta_p + 1$ epochs after acquisition and last for $\tau$ epochs.

This implies that at epoch $E$, the active FCUs were acquired in the range:

$$
E' \in [\,E - \tau - \delta_p, \; E - \delta_p - 1\,].
$$

Formally:

$$
\text{FCU}_{u,p,E}^{active} = \sum_{E' = E - \tau - \delta_p}^{E - \delta_p - 1} \text{FCU}_{u,p,E'}^{(acq)}.
$$

- If $\delta_p = 0$, this reduces to the simpler case where FCUs begin paying out one epoch after acquisition.
- If $\delta_p > 0$, the start of the payout period is delayed, reflecting a claim on future fees as chosen by the pod’s parameters.

---

## Fee Distribution via FCUs

In epoch $E$, pod $p$ generates $FEE_{p,E}$ fees. A fraction $\alpha_p$ of these fees is allocated to FCU holders, but only those FCUs that have entered their active payout window:

Total distributable fees:

$$
\alpha_p \cdot FEE_{p,E}.
$$

User $u$’s fee share at epoch $E$:

$$
f_{u,p,E} = \alpha_p \cdot FEE_{p,E} \cdot \frac{\text{FCU}_{u,p,E}^{active}}{\sum_{u'} \text{FCU}_{u',p,E}^{active}}.
$$

If no FCUs are active at epoch $E$, then no fees are distributed to stakers, and the pod retains all of its fees for that epoch.

The pod-specific delay $\delta_p$ enable FCUs to reflect a forward-looking claim, starting at a time chosen by the pod. This flexibility allows pods to tailor their payout profile.

## Adjustable Fee Splits

Each pod $p$ sets $\alpha_p$. Pods may change $\alpha_p$ over time, subject to governance or protocol-defined rules.

- Higher $\alpha_p$: more fees to stakers, attracting votes.
- Lower $\alpha_p$: more retained capital for the pod.

NOTE: implementation considerations may reduce the actual features offered by the Reppo network.

## Summary of Epoch Operations

1. **Vote Allocation:** Users allocate veTokens to pods. Apply user-level diversity bonus and concentration penalty to get $V_{p,E}^{eff}$.
2. **Performance Check:** Calculate median fee $M_E$. Update $\mu_{p,E}$ accordingly.
3. **Emissions:** Distribute $R_E$ proportionally based on $V_{p,E}^{eff} \cdot \mu_{p,E}$. Users receive $\text{EmissionShare}_{u,p,E}$.
4. **Fee Distribution:** Pods generate $FEE_{p,E}$. Distribute $\alpha_p \cdot FEE_{p,E}$ based on FCUs.
5. **FCU Accrual & Expiration:** Users earn new FCUs each epoch. FCUs older than $\tau$ epochs expire.
6. **Early Unstaking (if attempted):** Apply the non-linear penalty. User forfeits unvested FCUs and unclaimed emissions.
7. **Adjust Fee Splits (if any):** Pods may adjust $\alpha_p$ to optimize their strategies.

---
