Currency idea: Block reward based on mining difficulty

Explodicle

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Quote from: t3a on October 06, 2011, 07:47:43 PM

Quote from: ?? on ??

We've been using a logarithm curve since before you started posting so I assumed you had at least bothered to skim through the whole thread before posting. Removed the chart to avoid further confusion.

The derivative of number of coins would increase as the difficulty increased.

if you're using log₂(x) as the number of coins per block and the number of blocks per time unit should be constant, then the formula for the number of coins per time unit as a function of difficulty would be

y' = log₂(x)

The anti-derivative of that would be

x*(ln(x)-1))
-------------
ln(2)

Conclusion:

The number of coins per time unit wold be growing.

You're right, my bad, I misunderstood you a little while ago and thought you meant coins per block would increase exponentially when you were really saying total coins in circulation would.

t3a

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Quote from: ?? on ??

We've been using a logarithm curve since before you started posting so I assumed you had at least bothered to skim through the whole thread before posting. Removed the chart to avoid further confusion.

The derivative of number of coins would increase as the difficulty increased.

if you're using log₂(x) as the number of coins per block and the number of blocks per time unit should be constant, then the formula for the number of coins per time unit as a function of difficulty would be

y' = log₂(x)

The anti-derivative of that would be

x*(ln(x)-1))
-------------
ln(2)

Conclusion:

The number of coins per time unit wold be growing.

Explodicle

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I would prefer to have no central authority for bounties. Other cryptocurrencies do that and it's really sketchy and I would not trust them.

That being said, if you're willing to centralize to maintain stability, you should at least run with it and have a chairman who decides when to increase the money supply.

cunicula

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The price level is the intersection of a demand curve and a supply curve. If the demand curve shifts downwards a little, you can maintain a stable price by reducing the growth rate of supply. This is your idea as I understand it. However, if the demand curve shifts downwards a lot, then price will still fall even with 0 coin generation. In this case, the only way to maintain a stable price is to take coins out of circulation, that is, destroy them.

cunicula

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I think this would be a major improvement. However, if the market cap is falling, the proposal has very little power to maintain price stability. Consider mandatory txn fees. In the event of a difficulty decline, I would suggest txn fee destruction to maintain the price level. In the event of difficulty growth, I would suggest collection of txn fees in a centrally administered development fund. The fund could be used for merchant and developer subsidies ("bounties"). This system would allow for more stable prices in the event of a difficulty decline.

Explodicle

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If we assume constant number of miners and constant spending on hardware and electricity, difficulty can be modeled d=c*2^(t/18), where t is time in months and c is some arbitrary constant. Plot the log of that to see payoff over time, it's linearly increasing, not exponential.

That's not to say we really want linearly increasing payoffs - one would further modify this function to set how the money supply increases over time. How exactly depends on your economic school. We could even aim to slowly reduce money supply increase similar to Bitcoin.

t3a

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Quote from: Explodicle on October 05, 2011, 07:53:46 AM

Quote from: t3a on October 04, 2011, 06:30:32 PM

Quote from: ?? on ??

Quote from: ElectricMucus on October 03, 2011, 11:53:20 AM

Not exactly e is quite unique in this matter, it's not really about the growth rate but rather about the "divisibility" of the currency in regards to spending. Base 2 is the second best choice for a physical currency, best is 3 however in our case we can exploit the base e which for a physical currency is just a idealistic assumption but in our case a practical possibility.

That sounds very vague to me. How does base e make a cryptocurrency more divisible than base 2?

Quote from: t3a on October 04, 2011, 12:18:25 AM

If the value/block was increasing and the target spacing was staying the same then you would have exponentially more coins as the difficulty increased.

I assumed you would have the target spacing decrease so there was a constant number coins being produced.

No, I'm not trying to make production either exponential or constant. If I wanted exponential I would use a linear relationship between reward and difficulty, like 1 coin per point of difficulty. If I wanted constant I would just make the reward 50 coins forever and be done with it.

Yes, that's what I'm saying.
If you have one block every ten minutes, then you have one block every ten minutes.

If the difficulty goes up, then you have more coins/block, but still one block every ten minutes.

This means that you either expect the difficulty to stay constant, or to go down. Otherwise you will have an exponentially increasing number of coins.

The number of coins per block is f(x). Just because x goes up exponentially does not mean f(x) does. For example, if he was using f(x)=1/x, then the number of coins per block would approach zero.

If that is true, his difficulty/reward chart is completely misleading.

Explodicle

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Quote from: t3a on October 04, 2011, 06:30:32 PM

Quote from: ?? on ??

Quote from: ElectricMucus on October 03, 2011, 11:53:20 AM

Not exactly e is quite unique in this matter, it's not really about the growth rate but rather about the "divisibility" of the currency in regards to spending. Base 2 is the second best choice for a physical currency, best is 3 however in our case we can exploit the base e which for a physical currency is just a idealistic assumption but in our case a practical possibility.

That sounds very vague to me. How does base e make a cryptocurrency more divisible than base 2?

Quote from: t3a on October 04, 2011, 12:18:25 AM

If the value/block was increasing and the target spacing was staying the same then you would have exponentially more coins as the difficulty increased.

I assumed you would have the target spacing decrease so there was a constant number coins being produced.

No, I'm not trying to make production either exponential or constant. If I wanted exponential I would use a linear relationship between reward and difficulty, like 1 coin per point of difficulty. If I wanted constant I would just make the reward 50 coins forever and be done with it.

Yes, that's what I'm saying.
If you have one block every ten minutes, then you have one block every ten minutes.

If the difficulty goes up, then you have more coins/block, but still one block every ten minutes.

This means that you either expect the difficulty to stay constant, or to go down. Otherwise you will have an exponentially increasing number of coins.

The number of coins per block is f(x). Just because x goes up exponentially does not mean f(x) does. For example, if he was using f(x)=1/x, then the number of coins per block would approach zero.

t3a

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Quote from: ?? on ??

Quote from: ElectricMucus on October 03, 2011, 11:53:20 AM

Not exactly e is quite unique in this matter, it's not really about the growth rate but rather about the "divisibility" of the currency in regards to spending. Base 2 is the second best choice for a physical currency, best is 3 however in our case we can exploit the base e which for a physical currency is just a idealistic assumption but in our case a practical possibility.

That sounds very vague to me. How does base e make a cryptocurrency more divisible than base 2?

Quote from: t3a on October 04, 2011, 12:18:25 AM

If the value/block was increasing and the target spacing was staying the same then you would have exponentially more coins as the difficulty increased.

I assumed you would have the target spacing decrease so there was a constant number coins being produced.

No, I'm not trying to make production either exponential or constant. If I wanted exponential I would use a linear relationship between reward and difficulty, like 1 coin per point of difficulty. If I wanted constant I would just make the reward 50 coins forever and be done with it.

Yes, that's what I'm saying.
If you have one block every ten minutes, then you have one block every ten minutes.

If the difficulty goes up, then you have more coins/block, but still one block every ten minutes.

This means that you either expect the difficulty to stay constant, or to go down. Otherwise you will have an exponentially increasing number of coins.

t3a

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Quote from: ?? on ??

How would it change confirm times? nSubsidy and nTargetSpacing have nothing to do with each other.

If the value/block was increasing and the target spacing was staying the same then you would have exponentially more coins as the difficulty increased.

I assumed you would have the target spacing decrease so there was a constant number coins being produced.

ElectricMucus

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Quote from: ?? on ??

Quote from: ElectricMucus on October 03, 2011, 08:15:22 AM

I like the idea of a logarithmic inflation curve and thought about that myself.
You pretty much want to approach the natural logarithm with it and model the rewards to meet it.

What do you mean by "approaching" the natural logarithm? There's no difference in using base e, base 10 or base 2, the reward growth rate slows down at the same pace with any base.

Not exactly e is quite unique in this matter, it's not really about the growth rate but rather about the "divisibility" of the currency in regards to spending. Base 2 is the second best choice for a physical currency, best is 3 however in our case we can exploit the base e which for a physical currency is just a idealistic assumption but in our case a practical possibility.
see this article: (I have to admit I might not have fully understood it and this might be a wrong assumption, but you might look into it )
www.americanscientist.org/issues/pub/third-base

ElectricMucus

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I like the idea of a logarithmic inflation curve and thought about that myself.
You pretty much want to approach the natural logarithm with it and model the rewards to meet it.

If done right this could give more long term stability since economical development follows the natural logarithm.

Explodicle

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Quote from: d.james on October 02, 2011, 06:53:03 PM

what about: Coins mined during a higher difficulty is worth more than coins mined during lower difficulty.

That would make it difficult to price goods. More coins of equal value accomplishes the same thing, but you could be more certain how much they're worth.

t3a

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This would change confirm times, but if confirm times were quick like with Geist Geld then it could work well.

Correct me if I'm wrong, but it would have to be a linear relationship between difficulty and coin/block rather than exponential like you have in that chart. Otherwise you would the number of blocks/(arbitrary time unit) go down exponentially.

Bobnova

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6990 isn't 18 months newer than 5970.
Wait for the 7990.

d.james

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Firstbits: 12pqwk

what about: Coins mined during a higher difficulty is worth more than coins mined during lower difficulty.

Explodicle

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Quote from: ?? on ??

Most impressive. So I guess we should continue with nSubsidy = log(difficulty) for the purpose of discussion? Raise hands if you prefer logarithm.

(Raises hand)

johnj

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From what I've read about the 7x series, it'll give (very roughly) 1.25x more mh/s, while only requiring half the power.

IIRC, 800 ALU @ 50w, 1600 ALU @ 90w (where as the 5770 is 800 @ ~100w and the 5870 is 1600 @ ~200w)

(i may have some of my numbers mixed up, but i believe that's the jist)

ArtForz

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Doesn't sound too far-fetched, wouldn't be terribly surprised if the biggest single-GPU card ends up around 3.2-3.5Mh/J or so and a downclocked dual-GPU variant at least close to 4Mh/J.

ArtForz

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http://en.wikipedia.org/wiki/Koomey's_law

Topic: Currency idea: Block reward based on mining difficulty (Read 2514 times)