After studying those multiple-item dutch auction I think it is indeed exactly my model here. It is the same system eBay uses when you are not selling 1 copy of an item but 100 at once - and eBay ensures the rules I would like to see satisfied (i.e. you will never pay more on eBay just because you set a higher maximum bid initially). Here the pool is selling space (consisting of many 10^-8 NBT units) within the target for a price which is given by the interest rate.

In general you can say if you have increasing price levels p_1 … p_n, a target of T and a current liquidity of L then the pool has to pay (this forum needs a LaTeX plugin):

```
p_n * L for L <= T
p_n-1 * (L - T) + p_n * (2T - L) for T < L <= 2T
p_n-2 * (L - 2T) + p_n-1 * (3T - L) for 2T < L <= 3T
...
p_n-i * (L - iT) + p_n-i-1 * ((i+1)T - L) for iT < L <= (i+1)T
```

At each price level q the corresponding payout then should be distributed according to the liquidity provided. So if there are M participants with liquidity u_1,…,u_M then we normalize the liquidity to r_m = u_m / z with z = \sum_i u_i such that they sum up to 1 and then credit the corresponding part of of the paid liquidity as payout:

```
(L - iT) * r_m * p_n-1 if q < p_n-1
((i+1)T - L) * r_m * p_n if p_n-1 <= q < p_n
```

Every unpaid residual is then shifted to the previous price level and will be compensated there if the minimal interest rate is small enough.

Example:

So here L = 25, T = 20 and the price levels are: p_1 = 3%, p_2 = 4%, and p_3 = 5% (pool max) with n = 3.

So T < L < 2T and i above is 1, and the total payout is:

```
4% * (25 - 20) + 5% * (40 - 25) = 0.95 NBT
```

The 15 NBT at price level 3 will be compensated at 5% according to the contribution w.r.t. the total liquidity, so A and B both will get

```
5% * (5 / 25) * (40 - 25) = 0.15 NBT
```

while C will get

```
5% * (15 / 25) * (40 - 25) = 0.45 NBT
```

Both A and B still have 5 - 15 * 5 / 25 = 2 NBT at price level 2 (4%) containing 5 NBT, which results in an additional payout for A and B of

```
4% * (2 / 4) * (25 - 20) = 0.1 NBT
```

**Case 1: A changes its minimal rate from 2 to 3%**

No effect, neither price levels nor set of participants within a price level changed.

**Case 2: A changes its minimal rate from 2 to 3.5%**

New price levels: p1=3.5%, p2=4%, p3=5%. There is no change in the payout, since all coins will be compensated up to price level 2.

**Case 3: A changes its minimal rate from 2 to 4.5%**

New price levels: p1=4%, p2=4.5%, p3=5%. The 15 NBT in p3 will be compensated just as before, but now B and C are sharing level p2, giving B 0.05625 NBT and C 0.16875 NBT. So A will lose all payouts of the price levels skipped through the interest rate change.

**Case 4: B changes its minimal rate from 3 to 4%**

A is now alone on the 4% price level and will get the whole 5 NBT compensated at 4%:

```
4% * 5 NBT = 0.2 NBT
```

which accordingly gets subtracted from B’s payout.

**Case 5: C changes its funds from 15 NBT to 11 NBT**

L becomes 21 and only 1 NBT will be paid at 4%. C only reduces its own contribution to the last price level by changing the funds by this amount, therefore decreasing its own payout.

**Case 6: C changes its minimal interest rate to 0.01%**

New price levels: p1 = 2%, p2 = 3%, p3 = 5%. A and C are both now taking over coins from a higher price level to a lower price level. As before, C gets 15 * (15 / 25) = 9 NBT compensated at 5%, but now additionally gets a payout at previous price levels, therefore increasing its own payout. The one who is suffering from it is B, who loses the payouts at the second price level.

##NOW?##

So an increase of the minimal interest rate can only remove yourself from previous price levels which in turn can only reduce your payout (or it stays the same)

A decrease of the minimal interest rate can only add additional price levels where you get compensated and therefore can only increase your payout (or it stays the same)

Increasing your funds will always increase your contribution in the top most price level therefore increasing your payout.

Decreasing your funds likewise will only decrease your contribution in the highest price level and therefore reduce your payout.