5. Stake Capital Efficiency

5.1 Threshold

For the set of stakers we determine a threshold up to which stakes are not decayed. This is simply the geometric mean S ̄ of staking by each identited user Si :

Users can Stake in excess of Threshold but receive a capital efficiency decay since they are using Staking capacity which is a finite resource.

5.2 Capital Efficiency

A decay on earnings power is applied to stakes that exceed the threshold. This is designed to stop out sized Staking by single actors, but does not deter increased staking in general due to the other factors at play.

Since we only wish to decay stakes that are in excess of the Threshold, we define a discount factor, di , as follows.

The discount is transformed to a decay factor, λ.

The decay is applied to the excess capital and the capital coefficient of friction, μ, can be calculated.

For the purposes of αIMG allocations, we apply a weight, wi, defined as:

Equation adjusts the normal weighting by its capital friction and each Creator’s pool receives their proportional allocation based on the appropriate weighted stakes.

When friction has been applied, the surplus from the decay is sent to Treasury account (as opposed to rebalancing across all stakes).

5.3 Staking Outputs

The tables below display the effects of users staking at a constant nominal rate , increasing horizontally from left to right, vs. multiples of nominal increasing vertically from top downwards.

Figure 2: Discount Factor, d

Figure 3: Capital Efficiency Coefficient, μ

In Figure 4 we can see, for example, that if 50% of users staked 10× the nominal, they would experience ≈ 45% capital efficiency which would lead to half of the friction being taken away from the distribution (Figure 5), where distribution for this example is now ≈ 73%. The beneficiary of the friction is the Treasury.

Figure 4:Distribution Effect

Figure 5 below shows the effect on outsize stakes relative to the nominal.

Figure 5: Capital Efficiency vs. Stake Size

Whilst Figure 5 deals with relatively large multiples, smaller multiple have naturally much lower impact.

Figure 6: Smaller Multiples

Hence, we can see that Staking should naturally change in small increments across the board absent any material market changes.

5.4 Stake Vectors

5.4.1 Distribution Rates

The total amount of αIMG staked determines the distribution ratio.

Figure 7: Distribute vs. Burn

5.4.2 Outsize Staking

Outsize stake lose capital efficiency. Distribution is generally increased (increasing on staking), which increases capital efficiency for other Stakes directly and indirectly through burn (for all αIMG holders), whilst benefiting the Treasury.

Figure 8: Outsize Staking

5.5 Token Price

So far we have detailed and examined the effects of local benefits to staking. That is to say, the costs and benefits expressed in αIMG terms. However, a critical part of the choice of stake behaviour relates to αIMG price expressed in an external currency, e.g. USD.

Since all stakeholders are generally concerned with a rational USD return on capital, they must consider the price of αIMG relative to a perceived fair value as to how to balance their staking.

In simple terms, if αIMG is considered cheap, staking will increase since a distribution is more valuable than burn. Conversely, an expensive token will reduce staking as holders will want to liquidate αIMG into the burn.

The ability for αIMG holders to discern price justifies the existence of capital efficiency decays at the local level. For example, a αIMG holder may take a decay on capital efficiency to capture the perceived discount on αIMG price to fair value.

The model has been designed to allow equilibrium αIMG price to be discovered from staking behaviour without ever needing to reference price itself.