Multi-Token Model

The previous model enables bApps to assign accounts’ weights for a specific token based on their obligations and associated risks. To extend this framework to scenarios where a bApp seeks security through multiple tokens, these weights can be combined to calculate the account’s final weight, $W_{k,i}^{final}$ In this case, the bApp should define a combination function tailored to its specific needs. Common examples include the arithmetic mean, geometric mean, harmonic mean, or any weighted variant.

For example, suppose a bApp uses tokens $d1$ and $d2$, and considers $d1$ to be twice as important as $d2$. Then, letting $W_{k,i,d}$ to be the weight of account $k$ in bApp $i$ for the token type $d$, it could use the following weighted harmonic mean function:

$\LARGE W_{k,i}^{final} = \frac{1}{\frac{2/3}{W_{k,i,d_1}} + \frac{1/3}{W_{k,i,d_2}}}$

In this context, the bApp should define a specific $\beta_d$ value for each token based on its risk tolerance. Also, an important observation is that, specifically for the non-slashable ETH form of capital, the participation ratio $(p_{k,i,\text{NS}}\text{ ETH})$ should be used instead of the weight function $(W_{k,i,\text{NS}}\text{ ETH})$, as this type of capital carries no inherent risk.