The capping of reward is also very interesting possibility. I started with technical analysis to find out at what age should the reward be capped. And I found out quite unfortunate thing: the reward capping will not help much.
The analysis: I downloaded current balances of all 405 wallets with more than 10,000 PPC from here. They represent 78% of all coins today. Each of these wallets can find a block in less than day if their coins are matured. Even with optimal POS difficulty 180[sup]*[/sup], all of them can find a block in less than 14 days. We can assume, that if the reward is capped at 90 days, all of these wallets can wait until day 90 (worst case day 76) and mint only then. In such case, every wallet will create 4–5 blocks per year, which in total is 405 x (4 or 5) = 1620 - 2025 blocks. There is 144 x 365.26 = 52597 blocks per year, so with 90 days reward cap, the top 405 wallets will produce 3% or 3.8% of all blocks, while they should create 78% of all blocks!! Increase in minting of 3% will not boost POS difficulty much. The reward-capping age we would need would be in order of few days, but this doesn’t go together with the initial days with zero probability (30 days today), which are necessary for another security reasons.
I think to solve the problem, it must simply not be possible to put too much coinage into a single block. There is more ways how to achieve that (none of which should involve too much technical complication or other obstacles for the rich wallets). Few ideas:
[ul][li]Do not consume all coinage, use only some part and return the rest to the stake. [/li]
[li]Do not accept stakes bigger than ~ 1000 PPC[sup]**[/sup] at all. If the wallet is configured to mint, let it automatically split the stakes for users with big stakes who want to mint.[/li]
[li]Do not use coinage at all. (I.e. constant per-block reward).[/li]
[li]Probably many more.[/li][/ul]
This was the main message. If you want to explore on your own, I give you this Google docs sheet with list of all list addresses. (Change anything, I have a copy.) To simulate all network, I assumed that there is 1112 addresses with 3279 PPC, 2795 addresses with 313 PPC and 4337 addresses with 38 PPC. (According to bitinfocharts.com I posted above. For example there is 1112 addresses with ballance 1,000 PPC - 10,000 PPC, so I used average balance for all of them.) If you do not want to dig too deep into the mathematics, just look at the yellow fields. Change the “Reward cap [days]” and then tweak the “POS difficulty” until “Blocks” is around 100%. (Because this is what would happen with POS difficulty in praxis).
[sup]* Optimal POS difficulty is achieved if all wallets mint all the time, not considering the coin maturing process. According to this document, number of minting coins can be calculated as
PPCminting = 4294901760 x POSdiff / (60 x 600)
The number 4294901760 is, as explained in the document, relating base POS difficulty 1 to probability per second, 60 is the maximum coinage weight of every Peercoin the attacker uses (alpha’ in the original equation) and 600 is the number of seconds between blocks (T in the original equation). From this follows that
Optimal POS difficulty = 60 x 600 x money supply / 4294901760 = 177.6 ~ 180
** This should be, of course, proportional to money supply, because the necessary size of a stake changes with inflation. So it should, more precisely, be something like:
Maximum allowed stake = Money supply / 21200[/sup]
