[quote=“masterOfDisaster, post:16, topic:2211”]Self-interest is more complex, than shown in your model.
It has to do with securing the owned Peercoins from loss/theft by not minting (potential total loss with unknown individual risk).
And it has to do with securing the owned Peercoins from loss in value by helping to secure the network through minting (potential total loss with unknown individual risk).
Both aspects are obviously contrary to each other as they require opposite actions.
And you can’t omit that second aspect of self-interest.
But which one is more important?
Well, that seems to be a highly subjective thing…[/quote]
I would like to offer small analysis on this. I agree with petar87 that there is tragedy of commons problem in minting, since it is rewarded only by compound interest. The conflict of the two contradicting self-interests posed by masterOfDisaster can be resolved if we show that the self-interest to secure the network suffers from the Dinner’s dilemma.
I see Dinner’s dilemma daily on my dormitory, where lives more than 1000 people and the utilities are completely included into rent. (Last remnants of communism 25 years after its fall in my country.) If I decide to use water and electricity without any considerations, I will monthly consume about $50 more in utilities. Of course, my actions raise the rent in long term, but my contribution to the rent raise is divided among 1000 people, so my would-be resource-wasting is penalized only by $0.05 - totally worth it. (Of course if everybody does that, the rent will be $50 higher - but the responsibility is shared - I cannot really affect what other’s do, unless I start anti-wasting campaign, or something like that.) How does this relate to the self-interest to secure the network?
The probability that actively minting wallet is hacked is constant for most stake-holders. Let us denote it pH. (If you are BIG stakeholder, you could be targeted specifically by the hackers, so pH would increase, but this only supports result of this analysis as I will show later, let us assume pH constant for now.)
Your contribution to overall security (probability of no successful attack against the network happens, pS) is proportional to (~)
pS ~ $ value of your stake / market capitalization
It is harder to raise the network minting rate by 1% if the money supply is higher. Now, you could argue that your stake simply increases cost of the attack by the price of your stake. While this is certainly true (and at first look it would seem that the factor 1/market capitalization should not be there), we mustn’t forget that the motivation to attack directly increases with market capitalization. So bigger network also faces bigger attacks. Your contribution to the security is relative to market capitalization.
You will mint simply if pS > pH. We can immediately see that if somebody owns 70% of all PPC, or maybe even 30% of all PPC, he will have strong motivation to mint even in absence of reward (or if he/she is rewarded only by compounding). But if lot of PPC is owned by small stake-holders (hard to say how small is the critical amount), their gain by the security increase is not worth the risk of being hacked.
One can also see, from the condition pS > pH, that if pH is higher for big stakeholders as they can be specifically targeted by hackers, it will only worsen the Dinner’s problem here, since it could also demotivate the big stake-holders from minting, even if they would have motivation to mint to secure the network under normal circumstances.
We can ask ourselves, what would happen if we had true 1% reward. If you are rewarded by
R ~ $ value of your stake * 1%,
you will mint if pS * ($ value of your stake) + R > pH * ($ value of your stake). Why is that? pS and pH are probabilities, but your gain/loss is multiplied by the $ value of your stake - if you own more, you lose more if the attack is successful. We can eliminate the stake value and write the condition for minting as:
pS + 1% > pH
Clearly, for small stake-holders, pS is very small, but if 1% > pH, they will still be motivated to mint, while they wouldn’t, if it was only for their self-interest to reduce the attack risk. (The estimates for pH are, of course, highly subjective and there will always be people who prefer high security of a paper wallet. We shouldn’t force anybody to mint too harshly.) I hope the argumentation is not confusing with too many equations. (Or flawed.)