Bribery Attacks on Bitcoin Consensus [pdf]
jbonneau.com
jbonneau.com
Yes, the main assumption being that burning such huge resources would in any way be recouped by a simple double spend.
A double spending attack, as the name implies, simply allows you to spend twice the same amount of bitcoins. Thus, "an attacker [who] can purchase mining power" needs to be able to do so at a lower cost than the value of the bitcoins he will spend for the second time. Obviously, considering the hashrate and the fact that you need around 51% of it, or, 30% of it according to some calculations, I can't envisage any scenario where such a cost would in any way be justified by simply spending your own coins twice.
Moreover, one has to consider that if such hashing power was used to simply do what it is meant to do, then the attacker would be supplied with fresh new bitcoins, probably to the tune of far more than any amount he can double spend.
That is why "the Bitcoin protocol is a stable Nash Equilibrium."
Miners with longer time preference are willing to tolerate greater difficulty increases and invest more in mining and generally will go out of business later than miners with shorter outlook. This creates a feedback loop which quickly leaves in business only the most hardcore investors doing mining. This provides a foundation for "rational behaviour", that is decision-making for long-term value of Bitcoin.
In other words, economics of mining leave among miners only the biggest believers in bitcoin driving out lesser believers. That's why in practice all miners are "honest" - all of them have dug the deepest hole possible, none is interested in short-term "profit" from double spending that would not return even a fraction of their investment.
GHash already conducted a 49% attack against a gambling site. https://bitcointalk.org/index.php?topic=327767.0 They blamed a rogue employee - but then the claim is no longer "miners would never do that, it wouldn't be in their self-interest" but "no single person at any mining concern would do that, it wouldn't be in the mining concern's self-interest even if it it was in their own". Which of course isn't true. (It isn't true in the wider financial system either, which is why regulations exist.)
So for instance, I could print a lot of bills and call them dollar2, and go to everyone in the world - except Bill Gates, and say:
"Hey, I have this new currency, it's the dollar2. Tell you what, I'll give you a dollar2 for every dollar you have. I'm going to do that to everyone except Bill Gates. I don't like him, so I'm going to keep half of his share of the dollar2, and burn the other half. Here's the catch, you have to commit to only recognizing dollar2 as the real currency for the next week. If I succeed, you'll be a little richer because of the deflationary effect of burning half of Bill Gate's share of dollars. If I don't succeed, you can go back to using the dollar, and I'll pay you a dollar for your trouble."
So in a very narrow, restricted way, the "rational" thing to do is to go along with this plan, and there we go, the dollar have been taken over. Obviously, such a plan would never work, but it's similar to the arguments against most proof-of-stake or even proof-of-work systems.