toy_vault_model

an educational example for the New Order founder bootcamp

This is a simple model of Vaults and Stakers earning Yield

Definitions

Staker

Each Staker $i$ is an actor having a balance $b_i$ of tokens and the Staker can stake these tokens in vaults (described below). Each Staker has its own expectation of yield $x_i$.

$I$ is the set or collection of all Stakers such that $i \in I$

Vault

Each Vault $j$ maintains a deposit balance $s_{ij}$ for each Staker $i$.

Each Vault $j$ holds a total amount of stake $S_j$ deposited by all Staker $i$ such that $\sum s_{ij} = S_j$

Each Vault has an incoming reward stream $R_j$ that is distributed amongst Stakers each epoch or time step.

$J$ is the set or collection of all Vaults such that $j \in J$

TODO: define how rewards are accounted for in the model

Relationships

Depositing

When Staker $i$ deposits an amount of tokens $\Delta b_i$ into Vault $j$, state is updated as follows:

The updated amount of stake in $j$ is:

$S_j^+ = S_j+\Delta b_i$

The updated deposit balance of stake $j$ is holding for $i$ is:

$s_{ij}^+=s_{ij}+\Delta b_i$

The updated balance of the staker $i$ is:

$s_{ij}^+ = s_{ij} - \Delta b_i$

The maximum amount $i$ can deposit is:

$\Delta b_i\leq b_i$

Withdrawing

When Staker $i$ withdraws an amount of tokens $\Delta s_{ij}$ from Vault $j$, state is updated as follows:

The updated amount of stake in $j$ is:

$S_j^+ = S_j-\Delta s_{ij}$

The updated deposit balance of stake $j$ is holding for $i$ is:

$s_{ij}^+=s_{ij}-\Delta s_{ij}$

The updated balance of the staker $i$ is:

$s_{ij}^+ = s_{ij} + \Delta s_{ij}$

The maximum amount $i$ can withdraw is:

$\Delta s_{ij}\leq s_{ij}$

Claiming Rewards

TODO

Reward distribution

Assumption: for the time being only consider one reward stream.

The reward at each time step $r_{ij}$ for each Staker $i$ from Vault $j$ is

$\forall i,\forall j: r_{ij} = \frac{s_{ij}}{S_j}* R_j$

Behaviors

Stakers