(note: I'm using hashrate and difficulty as interchangable numbers to simplify things)
It seems that while a very high hash rate is good for the health and security of the network, a rate that's too high makes it too difficult for new miners to get into the game. Eventually, all mining will be controlled by a few super-sized pools that may have to take drastic measures to prevent overtaking the network (look at ghash.io).
What if there was a coin with an ideal hash rate set to a number. I'll use 1PH/s for illustration purposes.
Now, let's put this into a logarithmic scale, with the ideal hash rate being 0dBh:
Target = Log10(10^15)+150 = 0dBh
Any actual hasing above or below that target, would only be able to mine a discounted reward. The discount would be a function of the total hashing power expressed in dBh:
Rate dBh Reward
1MH/s -90 10%
1GH/s -60 40%
1TH/s -30 70%
1PH/s 0 100%
1EH/s 30 70%
1ZH/s 60 40%
1YH/s 90 10%
So, if the network isn't at the optimum hashing speed, rewards will be appropriately diminished... all the way to 0% (fee collection only).
Next, to prevent hostile miners, the number of mining operations could also be be targeted. For illustration purposes, let's say we want 1000 mining operations (pool or solo). In order to maintain a balanced workload, each mining operation would need to operate at 30dBh below the network dBh.
If the network is already operating at -30dBh (1TH/s), each mining operation would need to operate at -60dBh (1GH/s). Any deviation would result in further reduction of the block reward using a hard percentage as a modifier. Here's what happens if this coin starts with a single mining operation with 1GH/s capacity:
Network Goal = 1PH/s = 0dBh (50 coin base reward)
Network Rate = 1GH/s = -60dBh (50*40% = 20 coins)
Pool Goal = 1MH/s = -90dBh (inherited 20 coin base reward)
Pool Rate = 1GH/s = -60dBh (30dBh over goal) (20*70% = 14 coins)
With a single mining operation generating -60dBh, you have a difference of 30dBh from it's pool goal. This means a further 30% reduction in the reward it can claim.
Double that miner's hashrate to 2GH/s, but the reward only goes up a little. The network base reward is reduced to 43%, or 21.5 coins. The solo miner would further reduce that reward by 70% to 15.05 coins. A 1 coin increase for double the hashing power.
Anyways, I'm not done proofing the math involved, but I think that basing the rewards on a logarithmic scale would provide superior network longevity.
Thoughts? Comments? Anyone interested in starting a project with me?