Bitcoin Forum

http://www.scribd.com/doc/182399858/Cunicula-s-game-theory-primer-pdf

See the above pdf.

Note that I also think bitcoin is broken, so if anything I have a horse on the opposing team. However, these guys are completely wrong. I mean completely wrong as in go back and get an academic degree before you write white papers wrong. They deserve to be treated with far more derision than they have received up till now.

Perhaps computer scientists simply aren't as mean as economists? (I hope this is the explanation.)

Can you elaborate on why you think Bitcoin is broken?

If you add additional realism to the model, the rewards from cheating should depend on block reward. I ignored this to avoid confusing people.

A 51% attack allows imposition of monopoly fees generating miner revenue.

As block reward slowly approaches zero, the revenue from behaving honestly could go to near zero.
The revenue from cheating does not go to zero however, precisely because monopoly allows you to jack up fees.
The fees remain jacked up permanently as long as people play selfish.

Right now the block reward is really massive so there is no strong incentive to jack up fees (even if you could).
There should be some point where the block reward gets so low that conspiring to raise fees looks attractive.

This would happen a long time from now. I used to worry about this a lot under GPU mining, but feel better now that ASICs are in play (with many manufacturers). With specialized hardware I feel that we have many years to go before there is any danger.

The security of ASICs has nothing to do with their increased hashing power. It comes from the fact that they turn into expensive paperweights if bitcoin collapses. That keeps miners honest. GPUs have significant resale value. This tempts miners to cheat.

The fix is proof-of-stake which is a much stronger disciplinary device than ownership of an ASIC.

Sorry man, but you are embarrassing yourself now. There is absolutely nothing wrong with their conclusion under the common game theory assumption that miners are rational and atomistic. If bitcoin mining truly is decentralised, then the atomistic assumption has to be true. A really smart guy who is worth listening to when he is not in full-on confirmation bias mode explained it as follows :


Similarly a rational atomistic miner will neglect the effect his selfishness will have on the bitcoin price or the value of his mining hardware. He is simply too small to matter and the price is unlikely to be affected by his individual action. Even if he believes that the price will be affected, the net gain can always be made positive by holding a sufficiently large short position.

Thanks for pointing this out. As usual, I'm right in both cases, but I admit to being a little opportunistic in my exposition. I'm sure if you dig deeper you will find old posts conceding that hardware ownership mitigates the incentive problem. I never emphasized this before because it didn't further my agenda at that time. For this reason I was a bit torn about posting this. As I say in the beginning, I have a horse on the other side of the race.

The issue is liquidity.
You can sell off a small to medium-sized in investment in bitcoin very quickly.  Once you have a big investment this is no longer the case. You also do not need to hold bitcoin to conduct an attack (unless we move to PoS mining)

You cannot sell off your mining operation very quickly even if it is small to medium sized. You do need to hold mining equipment to conduct an attack.

Anyways, you go through a year of post history to try and attack my argument by impugning my character! Why not just meet me head on in battle if you are able?

Yes, if you can hold a sufficiently large short position this can cause problems. Same thing can happen in the vanilla stock market. That's why this stuff is regulated.
It is also why financial innovation caused huge problems. Value of derivatives issued on underlying assets >>> value of underlying assets ---> big incentive problems
No one is going to offer to insure huge short positions on bitcoin. The fact that someone is buying up huge short positions despite the incredible risk would tell you that you shouldn't sell them insurance.

Interesting how you are "right in both cases", but when others use the same assumption, they are "incompetent" and have a "fundamental misunderstanding of the incentives".


If you assume that miners are atomistic, then the size of the investment is irrelevant, because the miner assumes that the attack will succeed or fail independently of whether he cheats. Therefore ANY consideration of the attack's impact on the valuation of any of his assets is erroneous. It is like trying to consider the effect of a possible crash of the stock market on my net wealth, when trying to decide whether to have egg or cereal for breakfast. Erroneous, not because I will be able to offload my shares fast enough, but for the more fundamental reason that the market will do what it does, for better or worse, irrespective of my choice of breakfast.

If miners are not atomistic, then bitcoin is not decentralised.


Nope, not really, I wanted to use the atomistic assumption in a counter-argument, but I couldn't remember where I had seen it defined. Forum search and voilla, guess who?

Sigh, reread the pdf I never make any assumption about whether miners are atomistic or not. It doesn't matter for my argument.

It ABSOLUTELY mattters. If miners are atomistic, then your entire argument falls apart. Take for instance :


The miner considers the probability of his hardware dropping in value as being independent of his decision to join the attack or not. Any subsequent consideration of hardware value when making the decision to mine selfishly or honestly is an error. The only way that this is not an error is if you claim that miners are not atomistic. But that is equivalent to saying that bitcoin is not decentralised.

That is an assumption. The nash equilibrium stategy I described is based on mutually assured destruction. Basically, if anyone ever behaves badly, (even one atomistic guy once), then all miners will behave badly forever and forever. Since there is no threshold for bad behavior an atomistic miner, a small or even atomistic miner has the same marginal affect as a large-scale miner.  

This is just one equilibrium and is usually used as a model case because it maximizes social welfare. The folk theorem tells us that an extremely wide range of positive equilibria are possible in this setting. Basically anything is possible it is just that the equilibrium I described (the hair trigger equilibrium) is the best you can do.

Huh??? Are you drunk? I have been selfish mining with my CPU for the past 30 seconds, so I guess we're all F#@#ed now. Sorry guys, I must have misunderstood something somewhere.

The folk theorem tells us that if one set of nash equilibrium strategies can sustain long-run cooperation, then there are infinitely many sets of equilibirum strategies that can sustain long-run cooperation.

I have provided a single set of strategies that is a nash equilibrium in the dynamic game. This implies that an infinite setmof strategies exists which can sustain cooperation. Different societies and groups use different norms to sustain cooperation. I can't tell you exactly how norms in the bitcoin community work, I can just tell you that they exist and that because of these norms we don't have to fear selfish mining.

You have falsified my example strategy using an empirical test. Now if you proceed to characterize the infinite set of stratagies and test them one by one, you will have disproven my argument...

Look up the folk theorem on wikipedia. I've tried to find online lectures on the topic. Found two , but the lectures are so abysmal that I'm still holding out for something better.


Here is a classic reference if anyone wants to go all hardcore. Reading this makes me feel so stupid...

http://www.eecs.harvard.edu/~parkes/cs286r/spring06/papers/fudmaskin_folk86.pdf (http://www.eecs.harvard.edu/~parkes/cs286r/spring06/papers/fudmaskin_folk86.pdf)

I'm sorry but your whole argument is flawed. You need to treat miners as atomistic and you don't. That invalidates everything that follows, so I don't need to read any further. Rewrite your paper while sober. Remove all consideration of the possible effect a successful attack could have on the value of the miner's assets. Get the payoff matrix for the prisoner's dilemma right, and then try again.

Whether they are atomistic or not is irrelevant. They can be arbitrarily small, e.g each miner has hashing power of 1 hash/year and so there are 10^12 individual miners. The argument still applies in this case. I don't think that we can define the meaning of 'miner' if we treat them as actually infinitesimal. Doesn't it strike you as absurd to base your your objection on the difference between a world with 10^99999 miners (where my argument applies) and a truly infinite number of miners (in which case behavior is poorly defined)? Is this distinction between a world with 10^99999 people and ∞ people really what stops you from agreeing with me? Or perhaps you are grabbing at any straw you can find to avoid acknowledging your humiliation.

You don't need to know who cheated, just that selfish mining happened in the last period.

There is a complication if you can mine selfishly in secret. (not keep your identity secret but keep the actual knowledge that someone is doing selfish mining secret)

Then there is a signal extraction problem, and you would set off the hair trigger punishment if the aggregate signal crossed a certain threshold.  There is a folk theorem for this too.

Do you want me to modify 'Cunicula's primer' to include the signal extraction problem?  I thought it would just confuse people with unnecessary complexity. Its not like I'm getting my point across with the status quo.

(Wait...on a second thought since selfish mining is assumed to snowball in the subgame there is never any signal extraction problem in evaluating play from the previous period. Why am I introducing an erroneous argument for you? I should really just set up a second account to argue with myself. It would be more productive.)


 

What payoff matrix do you want? One where selfish mining causes harm that doesn't operate purely through price effects? Sure I can introduce this, it would strengthen my argument.

You want me to get rid of price effects? How can we call selfish mining 'harmful' if we assume that it has no effect on future bitcoin prices? Okay, I can introduce that assumption, but doubt that assuming the user base is indifferent to centralization is reasonable. If it were reasonable, then selfish mining would not be a problem, so I would still be correct.

What I mean to say is how do we reduce the value of bitcoin without reducing the value of ASIC mining equipment? How would that work exactly? How do we have miner's that do not own any mining equipment?

As for writing this while sober... it is too difficult to face the stupidity of people like you while sober. I prefer to save sobriety for serious projects.

No, it is not. I am tired of explaining why, but you clearly did understand this in the past.

Economists employ models that are simplifications of the real world. The simplifications are not intended to capture reality perfectly, but instead highlight the most important aspects. Yes, this allows us to engage in some strategic doublespeak when we see fit. However, in this case, I think the context has become quite different.

In a world of ASIC mining, effects of the value of capital assets on miner incentives become important. It is completely unreasonable to assume that ASIC prices do not fluctuate wildly with the price of bitcoin. If so, miners will no longer be short-sighted.

In a world of CPU mining, (as I noted in the paper), they are not important. Botnets, home PCs, and such have competing alternative uses. It is extremely unlikely that bitcoin price movements would affect the price of CPUs. If so, miners will be short-sighted. (i.e. they won't suffer a drop in future hardware value if the bitcoin price falls)

In a world of GPU mining (which we lived in circa Nov 2012 when you are quoting me), things are much closer to the CPU case then the ASIC case. So I made this simplification. It's really important to the problem whether miner fixed costs come from illiquid capital assets or liquid ones. It was not unreasonable to treat GPU prices as independent of bitcoin prices, though I confess that this was an approximation. (i.e. miners won't suffer a meaningful drop in hardware value if the bitcoin price falls)

I was certainly well aware of how ASICs would change this at that time. I have long believed that ASICs would strengthen Bitcoin's security model in terms of miner incentives. On the downside though, I expect most of the hardware producers to get driven out of business and one or two productive firms to capture the market.
This is called a 'shakeout' and usually occurs after a boom in an industry starts to die down. The downside is that the surviving firms will gain a lot of control.

 

Errm, any correct one will do. For someone who passes himself off as a source of game theory knowledge it is more than a little embarrrasing to get the payoff matrix for the prisoner's dilemma wrong. If you can't see a problem with the matrix in your paper I suggest starting with
http://en.wikipedia.org/wiki/Prisoner's_dilemma


No, for the hundredth time. I fully accept that a successful attack will destroy bitcoin, as does the atomistic miner. The atomistic miner hopes to hell that the attack fails,but takes part anyway, since his contribution is too small to make a difference between success or failure. This can also be stated as :


Nice.

"When you have no basis for an argument, abuse the plaintiff."
— 'Cicero

Stop fighting a straw man. I never claimed that ASIC prices would be unaffected, just that this is immaterial to the decision of an atomistic miner.

ASIC values are pretty tightly coupled to bitcoin prices, but you know what is coupled even more tightly to bitcoin prices. bitcoin.


Reread that last sentence. In the absence of confirmation bias, you argued that even miners that were heavily invested in bitcoin would take part in an attack, since they were atomistic. Now you argue that atomistic miners that are heavily invested in bitcoin mining equipment won't take part in an attack. Why are the miners more easily swayed by the mining equipment that they hold  than by the actual coins?

a) you do not need to retain your investment in bitcoin to mount an attack. You can sell it first.
b) if some people have no investment, then they will always attack. If this is the case, the people with an investment will also attack.
c) If GPUs market price is not related to the bitcoin price then (a) and (b) will hold
d) If ASICs market price is closely related to the bitcoin price then (a) and (b) will not hold. You cannot attack without carrying an ownership stake into the next period.
Due to this constraint, the game can support a cooperative equilibrium.


(d) is the whole theoretical underpinning of proof-of-stake. Do you really think I would be unaware of this?


Curious. Are you suggesting that I am just using doublespeak on purpose? If not, how do you explain the perceived arbitrary reversal in my line of argument?

Okay then. Now we are getting somewhere. Define what you mean by atomistic in this context.

Does ownership of one USB miner count?
Or do I need to own an infinitesimal fraction of a USB miner to be atomistic?

If your answer is that only the latter counts as atomistic, could you explain why this case is relevant to understanding real world behavior. Doesn't the first case seem to have more real world relevance? If we find that I am right in the first case (I invite you to check the math), why would we care whether the results apply in the second case?

Aside: It's also really important that mining has become more capital intensive with the arrival of ASICs. If we have mining where capital costs are negligible and electricity is the only important expense, then we would be in trouble.

I promise to do some bedtime reading of that, now that I've given Scribd my email and personal biometrics in exchange for the pdf.

To me it sounds like people are getting so tied up in details like: how hardware re-usability affects incentives, that it's easy to lose sight of context. Meanwhile, others are shocked that there exists an ecosystem of altcoins at all, and they're clearly fearful that this stealth inflation will dilute their profits https://bitcointalk.org/index.php?topic=279650.0 (https://bitcointalk.org/index.php?topic=279650.0). Plz bear with me while I try to summarise some coin evolution:

Communist coins (least evolved)
Anyone can make infinite coins for free. No scarcity, no relative scarcity. Basically no-one is 'fooled' into valuing them.

Proof of Work coins
Anyone can make coins, expensively. The production rate is continuously measured and then tightly regulated so that it follows some horrible arbitrary-looking scheme. The game seems to introduce scarcity, and because the coins are unevenly scarce, lots of people value them. However, altcoins and liquid exchanges can dilute this scarcity, though I admit it seems like a formidable task predicting just how network effects and a first mover advantage might play out in a future. At least "communist coins 2.0" doesn't seem likely, since there seem to be distinct elements of meritocracy at play (more about that in a moment).

Proof of Stake coins
I'm rusty on the details, but IIRC they fix a bunch of perverse incentives, by promoting a monopoly coin rather than an unhealthy ecosystem of coin-hopping speculators. And the production cost is low, which gives a PoS based economy a competitive edge ahead of PoW money. The lesson seems to be that the scarcity doesn't have to be 'real' with costly PR in the form of a PoW mining game. As long as the coins are relatively scarce, having trusted stakeholders seems fine. (And they could probably fine-tune the system by controlling velocity by managing transaction fees).

However, if I'm correct that PoS coin would trend towards a monopoly, then lending becomes a problem. Fractional reserve in the form of a pyramidal banking hierarchy is highly inefficient: every time an end-user wants to borrow money, the banking hierarchy creates friction by adding their own (usually enormous) costs at each level. Compare that to something like this:

A business wants money for some venture. In order to overcome the lending problem (what units do they borrow to fund their business??) they issue high-tech shares that are somehow added to a popular currency that represents a basket of various participants' shares. But how to do it? Perhaps something like:
the business registers itself as a participant on a blockchain somewhere.
the business releases 'old' coins, while everyone else's pre-existing coins are automatically devalued slightly with the new shares. The transparency prevents stealthy, dishonest inflation*. And there is no longer any need for lending. *The idea is of course incomplete. There would probably need to be additional incentives to prevent excessive inflation, perhaps some system of dividends. This is where we should be focussing our efforts. Proof of stake is still nibbling around the edges.

and the fees MUST remain competitive to alternative payment networks.  If it's not cheaper than eg. Paypal then Bitcoin is useless, less adoption, even more problems for Bitcoin valuation.  Seems like all the problems will hit at once.

Yes, it's not so useful for society in the long-run, but it could still survive. Consider this scenario
1) bitcoin offers low fees for a long time
2) the user base grows tremdenously due to these low fees
3) competing systems like paypal are driven out of business
4) coinbase finances a 51% attack raising fees for on the chain txns to monopoly levels
5) coinbase raises user fees for off the chain txns, but they remain competitive with paypal like operations

Coinbase could be very profitable. Since coinbase is doing price discrimimation, this is actually a more efficient strategy for extracting monopoly rents than the system used by paypal. What you would end up with is a beefed up monopoly. It doesn't necessarily mean the death of bitcoin.

while I think some of these sub-scenarios are possible, I dont think Bitcoin will run Paypal out of business due to the legal/regulatory dimension.

I think that not enough people are talking about what the effects of a rise in TX FEES will be.  It's not just a simple function, once it exceeds a certain limit(the cost of using more traditional payment networks) then there will be catastrophic results.

something like this:

1) TX fees make Bitcoin more expensive than Paypal
2) People stop using Bitcoin
3) Demand for BTC greatly decreases
4) Price of BTC greatly decreases
5) Miners no longer participate
6) Less processing power, more expensive transactions GOTO step 2

just a rough scenario...

Freicoin addresses the slow dwindling of BTC block rewards and dependence on transaction fees by use of a Demurrage system that supports perpetual block rewards while maintaining a fixed monetary base.  Demurrage means all currency holders pay for the network security rather then just transactors.  If not for the crazy gold-bug nature of the anarcho-libertarian world view this solution would have been blindingly obvious at the design phase of BTC.  We think people will eventually come around to realizing Demurrage is the only sustainable basis for a PoW currency and it also has positive price stabilizing and interest rate reducing effects too.

Yeah, I agree that perpetual demurrage has you covered, so would perpetual money supply growth. We talked about this before remember? You asked me what money supply growth rate I would pick for a cryptocurrency and I said a fixed single digit percentage that is invariant over time. That's equivalent to fixed rate demurrage for most purposes.