HDG tokens are primarily used for revenue sharing. Anyone who stakes the HDG token is able to claim a proportion of all protocol fees. As the Hedge protocol evolves (with new functionality such as accepting different types of collateral), HDG tokens will be used to vote on governance and use of treasury funds.
The protocol, and in turn HDG token holders, earns fees when:
Depositing USH in the stability pool. The formula for the total amount of HDG rewards released is the following:
f(x) = 2,000,000 * 0.5^(x/365) / (365/log(2)), where x is the time in days. This can be visualized here.
Effectively, HDG token incentives are large at the initiation of the protocol but will gradually decrease over time. The more USH you deposit in the stability pool and the longer the USH is deposited, the more HDG you are rewarded with.