Influential Peers
Modeling relative influence of peers in the Local network
A portion of transaction fees is redistributed back amongst token holders as rewards for adding value to the network. We model relative influence of peers in the token economy based on the sum of their edge weights (held tokens from prior transactions) and their eigenvector centrality ranking (relative influence).
Circulating supply: Suppose there exist a total of $T$ Local tokens in circulation. We define the Circulating supply, $S_t$ as this number of token, plus the token value of the entire graph,
Total network revenue: We define $R_t$ as the total amount of revenue the network collected from time $t  \tau$ to time $t$. The period $\tau$ is some network parameter, which controls how often rewards are given out (for example these can be given out daily, $\tau = 1d$)
Producer rewards: Suppose there is a producer $u$ who has a graph value of $G_u$ and holds $t_u$ tokens. We define $r_t^u$ as the rewards the user will receive at time $t$ for the period between $t  \tau$ and $t$. These rewards are given by,
$r_t^u = R_t \left(\frac{t_u + M_t(G_u)}{S_t}\right).$
Reward distribution method: Suppose the network revenue $R_t$ is collected from users in FIAT currency. There are three possible methods to deliver these rewards to the token holders.

Redistribute in FIAT. Every token holder receives their rewards in FIAT currency.

Redistribute in Local. The revenue $R_t$ can be used to buy an equivalent amount of Local tokens at current market rate, and then give this as rewards to token holders. This has a benefit of adding buy pressure for the Local token itself.

Burn Local. The revenue $R_t$ can be used to buy an equivalent amount of Local tokens at current market rate, and then burn this. This rewards Local token holders in that it creates deflationary pressure on the Local tokens they already own. This has an advantage of being easier to implement, we can simply send the burned tokens to the 0x0 null address.