Good questions! Let's see if I have good answers. Really my goal isn't to prove I'm a genius. Or that I've already got all the perfect answers. I came back here to have a discussion about concepts like these.
Hmm I'm still confused about how difficulty scales in your system. Why can Charlie win at most 10 times in a row? And what do you mean by doubling his "personal" difficulty?
For convenience of discussion I'm proposing a proof-of-work function similar to bitcoin's. They each miner tries to get their new coin transaction *blessed* by random chance. They do this by repeatedly hashing the transaction and a random (or sequential) nonce until the result meets the current difficulty requirements. In bitcoin's case this means a minimum number of consecutive zeros in the most significant digits.
So if the difficulty level is 1 the most significant digit must be zero. Exactly 1/2 of the possible hash result meet this requirement.
If the difficulty level is 2 the two most significant digits must be zero. Exactly 1/4 of the possible hash result meet this requirement.
If the difficulty level is 3 the two most significant digits must be zero. Exactly 1/8 of the possible hash result meet this requirement.
And so on, each time you increase the difficulty by 1, you double the average number of hash trials it will take to find an acceptable solution.
So, if Charlie doubles the difficulty ten times in a row, he has used up all of his computational advantage. 2^10=1024 He has in effect rescaled the game to put himself in the same situation that Alex and Bill were in before he arrived.
"Doubling his personal difficulty" does sound misleading. My bad. I meant by doubling *everyones* difficulty, he also disadvantages himself.
In your proposal it says that difficulty retargets to current+1 if a proof-of-work+1 transaction wins and goes down to current-1 if no proof-of-work is submitted, so wouldn't it be better for Charlie to pump up difficulty to monopolize and then just mine proof-of-work+1 one block then stop the following block to bring difficulty down, rinse and repeat?
This is an interesting situation. I think you are correct in your analysis. But let's discuss what I was intending, where I messed up, and where it could be fixed.
You had said something like, "in the future, processors might be 1000x more efficient." I totally agree with your premise. They certainly will. I was being a bit of troll, however, when I made the example. I actually started with 8x more powerful, but that didn't seem very hyperbolic. So I went to 32, 64, then I said fuck it. Go big or go home! 1024 times was a big jump over his competitors all at once. It leaves room for a few examples I didn't consider.
A big Woot! to you for finding one. Woot!
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You are correct, he could win say 5 times in a row to price his competitors out of the game. He could then quit mining knowing that *no one* could compete and the difficulty would fall back -1 where he could mine and win +1 again as you stated. Of course his competitors would all notice and start looking for upgrades... But that would be an unnecessary tangent to your more interesting question.
I had intended for the +0 level to prevent this. By offering a +0 tax refund, I was hoping to make it profitable enough for those with taxed transactions to each commit *some* effort to mining. This creates an ad-hoc mining pool. If any of them wins, all of them get their tax refund. I had intended this pool to *never* get priced out of mining, except when the economy was actually falling.
I also tried to compensate for situations like this using the ration between the -1 tax and the +1 bonus of (1/2 * tax). If the system starts to oscillate, the number of coins actually falls rather than staying the same. Eventually, I thought, this will cause enough inflation so others could get back in the game. However, 2^10 leaves enough room for Charlie to price *everyone* back out again.
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The saving grace for me, is that even with Charlie taking control in a different way, the system didn't bubble or bust. The ENC value is still relatively stable. Except for the inconsistent taxing, network clients wouldn't even notice the difference.
The process doesn't care who gets rewarded in dollars. Its goal is keeping the value of ENC stable and it succeeds in this scenario.
In fact, it is in Charlie's best interest to move the market as little as possible. In the above example I said, "he could win say 5 times in a row to price his competitors out of the game." But, if he could price all competitors out by winning only 3 times in a row, his arbitrage gains would greatly increase. No sense for Charlie to spend 4 times the electricity if he doesn't need to.
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Ironically, for me, if Charlie adopts this strategy, he in effect implements the proposed EnCoin transaction fee I've been lobbying against! This fee takes coins from the spenders, destroys them, then recreates and gives them to miners. All while minimally effecting monetary policy. Ugg!
Charlie is promising to keep everyone's monetary policy stable, in exchange for a small fee! It only seems like a scam because monetary policy would be even more stable without Charlie's actions and fees. Go figure?
