How much money would it take to bribe the majority of miners to attack the system?

I think this question is just a re-formulation of the 51% attack, but it has me thinking: miners are monetarily incentivized to not perform a 51% attack, but there must be some amount of money will cause their incentives to switch. So how much is it?

It is commonly understood that miners have invested in equipment, and so doing something to harm the value of the cryptocurrency they're mining (ie, engaging in a 51% attack), undermines their investment.

But what if a very wealthy entity bribed the miners, external to the bitcoin system, with an amount that exceeds any returns the miners could possibly hope for? For example: a govt pays a majority group of miners \$X billion + electricity costs to just 51% attack the network with empty blocks indefinitely.

I think an attack like this could be effective in hurting the public confidence and price, but there are ways it could be thwarted too (switching the POW algorithm, for example). So I don't think it is dangerous in a fatal way.

So my question is: can we estimate how much money it would take to successfully attack the network in this way?

Cost of attack = [(51% of block reward + fees per year)-(cost of 51% of equipment purchased for the next year)-(51% of the network's electricity costs for the next year)] * (number of years worth of income it takes to bribe the miners?)

Am I missing anything here? Or making false assumptions? Interested to hear what others think

• The miners, assuming they are rational, will demand as much money as they will lose from having their ASICs turned into expensive space heaters. Commented Dec 4, 2017 at 11:24
• @DavidSchwartz This is only true, when they can't use their hardware to do better things, maybe they can mine an alt coin. But also if they demand so much money I can give it to them, if I hold a large short position on the coin, as it is mentioned in my theoretical attack scenario.
– user65934
Commented Dec 4, 2017 at 12:51
• @sigmabe But they can't use their hardware to do better things. These are ASICs that only do one thing. And they couldn't mine an alt coin because such an attack would cause every coin that uses their algorithm to either crash in value or change their algorithm. Commented Dec 4, 2017 at 17:22
• @DavidSchwartz The problem is maybe that there isn't a good alt-coin today using a proof-of-X construction which is resistant against this form of attack and can be mined by ASICs. But maybe tomorrow there is such a coin...By the way, there are other coins you can attack for example Monero.
– user65934
Commented Dec 4, 2017 at 17:43
• @sigmabe Not sure I follow. If there's a way to resist this attack, then every PoW coin can adopt it. If there's no way to resist this attack, then it makes the ASICs worthless. Commented Dec 4, 2017 at 17:46