In this post lets understand the payment for mining and what measures are taken to ensure a fair distribution of reward.

Miner Payment forumla

This is the equation for Payment to a miner for completing an AI computation. The formula is from page 7 of the white paper. The powers of 1/d makes it a little non-intuitive to understand the equation. In the rest of this post I will break it down to understand what the formula does.

In the equation t is the AI task given for miners to solve, m is the miner, Q is Quorum, which collectively stands for all the miners performing the task, t. The payment for the miner, m is dependent on the stake, Stake(m) he/she has. Bid(t) is the amount that is bid in the market place for completing the task. Hadron has some operational costs, OperatingCost(t) for managing the task, t and it is deducted from the bid amount.

The amount Bid(t)-OperatingCost(t), which lets call balance, is shared between the miners. The question now is how much share of the balance miner gets paid? To say in a nutshell, the miners with more stake gets slightly larger fraction of the balance. We don’t want the miners with large stake to get almost all the balance. This is enforced by the 1/d in the formula.

To get a sense of how the 1/d affects the distribution of balance, lets imagine that a task, t is assigned two miners m1 and m2. Stake of m1 is 9 (Hadron tokens) and stake of m2 is 100 tokens. Let the bid amount be 1005 tokens and the operation cost is 5 tokens. So the balance will be 1005–5=1000 tokens, which will be shared between m1 and m2.

Now let us consider two scenarios:

Scenario 1:

Without damping — d=1, i.e. 1/d=1/1=1

Mining Payment without damping

In this above figure, there are two pi charts. The first chart shows the reward/share in the balance for miners m1 and m2 if they have stake 9 and 100 respectively. m1 gets 83 tokens and m2 gets 917 tokens. The second pi chart shows the rewards for m1 and m2 if they have stake 9 and 10000 respectively. Here m1 gets 1 token, but m2 gets 999 tokens! We see that in the absence of damping factor (i.e. d=1), if a miner has a very very large Stake (10000 of m2 vs 9 of m1) he/she ends up taking up almost all the balance. This kind of situation does not provide an incentive for miners with small stake to mine.

Scenario 2:

With damping — d=2, i.e. 1/d=1/2

Mining Payment with damping (d=2)

In the above figure, the first pi chart shows the reward/share in the balance for miners m1 and m2 if they have stake 9 and 100 respectively. m1 gets 231 tokens and m2 gets 769 tokens. Notice that this pi chart is for the same situation as the pi chart in the first figure; the only difference is the existence of a damping factor here. m1 here gets more tokens for the same stake (9) i.e. 231 tokens in contrast to the 83 before. The second pi chart shows the rewards for m1 and m2 if they have stake 9 and 10000 respectively. Here m1 gets 29 token and m2 gets 971 tokens. Again contrast it with the second pi chart of the previous figure. Miner m1 gets 29 tokens here compared to 1 token in the case without damping factor. Hence, the damping factor can provide better returns for miners with small stakes without favoring the high stake miners very much.

Also note that as the value of d becomes very large, every miner gets almost the same share in the balance irrespective of their stake.

For Hadron, the damping factor, d is greater than 1. It is not yet known what the exact value will be.

Hopefully now it is clear how the payment is calculated for miners and the important role damping factor plays in ensuring fair distribution of the balance.