The Game Theory of a Bitcoin Strategic Reserve

The United States throwing its weight behind Bitcoin would effect a massive shift in the game theory underpinning Bitcoin, but probably not in the way you think.

Bitcoin's decentralized consensus mechanism works based on some cleverly crafted incentive structures. The first and fundamental rule is that the chain with the most work is the correct one. This single rule obviates the need for a central arbitrator, determining which chain is correct as function of the efforts of thousands of decentralized parties, each trying to extend the block. The subsidy to miners keeps moving the blockchain forward, creating painful opportunity costs for miners who don't mine the tip. These mechanisms, together with the difficulty adjustment, set the game theoretical framework for a chain that has marched forward, 1 block at time, with near 100% clarity for the last 15 years.

The only caveat is that if one miner or coalition of miners is able to marshal more than 50% of the hashrate, they will have the ability to overwrite recent blocks, prohibit other miners from writing future blocks, and determine which transactions are recorded in the canonical ledger. This would be a disaster, obviously; the entire point was to avoid a situation in which a single party was in control. So the ultimate binding piece of the game theory designed by Satoshi is that there is some incentive to prevent this from happening. As described in the whitepaper:

The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.

He ought to find it more profitable to play by the rules

Indeed, this is the bedrock for all of the game theory in Bitcoin. Bitcoin makes sense if and only if, at any point in time, at least 50% of the miners are incentivized to stay honest. This has been the case since 2009.

An underdiscussed, but perhaps most crucial part of the theory is the reason why he ought to find it more profitable to play by the rules. The answer, in 2009, 2010, 2011, and every year since has always been the same: Because if he didn't, it would break. If it breaks, the Bitcoin experiment is over and the miner who did this would become proud owner a landfill full of worthless E-waste. This is what Satoshi was referring to, and this is why the community panicked in 2014 when the ghash pool exceeded 50% of the hashrate. The idea that one party (even if that is a pool) could take over the system represented such a disastrous failure mode that everyone tries to avoid it.

Built into the game theory is the understanding that theoretically someone could, perhaps with significant costs, direct over 50% of the hashrate to behave in a dishonest way, forcing a constitutional crisis. But the natural result of this crisis is mutual assured destruction for all miners and holders. This is the ultimate deterrent for misbehavior.

Note that the theoretical possibility of a 51% attack is eternally present, regardless of the current hashrate, costs of electricity, cooling or new ASICs. This is a tautological consequence of the fact that 51% < 100%: At any point in time, a pool could be created with malicious intentions, and 60% of miners could join this pool. The fact of the matter is that in recent times, 100% of the miners are electively mining the tip. It is always a matter of incentives, not physical plausibility.

For those outside the system, who own no ASICs, the security model prohibits them from attacking the system. But the security model is designed not only to protect from external threats (it's an open system after all) it's designed to protect from actors `within' the system as well. Miners don't just protect the system from non-miners, they protect the system from other miners.

Consider selfish mining. This technique is mathematically demonstrated to give an advantage to a group of 34% of miners who executes this technique beyond a difficulty adjustment period. Selfish mining doesn't involve explicit stealing or even censorship, just a better ROI for the miners who would form the coalition. Recent reports have put the miner share of the top publicly held mining corporations at close to 30% and growing. Toss in a few large private miners and we get to selfish mining threshold. Does it seem like selfish mining is inevitable? All that is required is that a collection of miners comprising 34% to hop on a call and start the process; three weeks later they're reaping the rewards. Yet so far no groups of miners have made an attempt to do try this. Why is this?

Selfish mining would represent a major norm violation; crossing this line would lead Bitcoin into a nasty place where competing groups are slugging it out. The grand prize for the winner is monopoly control, under which the monopoly miner gets to keep all the fees and block subsidies, can ease down their hashrate to boost profits, and can even negotiate fees directly or even set their own fee rates. But this would be a disaster for Bitcoin; for this reason, nobody is initiating that call.

I wrote a chapter in my book about coalitional game theory, analyzing exactly this problem in regards to monopoly mining. The analysis boils down to a comparison of the profits accrued to a 51% coalition which splits the rewards from a monopolized chain, or the small profits accrued to the grand coalition if they stick to the competitive course. In the early days, the answer was clear: Monopoly mining would have destroyed everything, so there is no incentive for a coalition to form.

Enter USG.

If the USG commits to a plan, over years and decades, to invest in Bitcoin, they will have created something which cannot fail. It simply cannot. Regardless of who mines Bitcoin, who is priced out, what parties use the chain, it cannot fail, and it won't fail. If there is a constitutional crisis about mining, this crisis will be resolved and resolved in a very clear and definitive way.

There are quite a few ways to resolve a constitutional crisis, when you expand your window to include centralized options. In the early days these options would have been discarded as inferior to failure, but if failure is not an option, all options can and will be considered. A simple brute force assertion of 51% power by USG and US controlled miners is one option (this need not require censorial monopoly mining.) Another workable solution is a permissioned soft-fork which only allows new blocks by the publicly traded miners. Obviously, Proof of Stake is on the table. Another option would be to convert the UTXO set of Bitcoin into a CBDC whose transactions are confirmed by the Fed. This would bring Bitcoin to the masses at lightning speed and bring massive value to early holders.

The point is that under this regime, monopoly mining is no longer failure per se. Any coalition of miners could pursue monopoly mining, starting with selfish mining and snowballing their coalition to 51%. As long as they don't do anything that directly irritates the USG, they can't break the system. If they achieve monopoly mining, the USG is still there, backstopping Bitcoin.

In short, the USG enmeshing itself with Bitcoin's success decades into the future removes Bitcoin's ultimate weapon against centralization; its option to fail.

It's hard to imagine that miners who are fighting for tiny profit margins would continue with decentralization theater, when they ought find it more profitable to form a coalition and monopoly mine, which strictly speaking, isn't even against the rules.