A limit to Bitcoin scale?

Eric Budish has a new paper out on “The Economic Limits of the Blockchain.” He demonstrates a potentially fundamental contradiction at the heart of ‘proof of work’ schemes to support cryptocurrencies — the most famous of which is, of course, Bitcoin. It is an incredibly clear issue so I figured I would recount it here.

As is well-known, there is a ‘open entry’ mining game at the heart of Bitcoin which generates a reward, P_block, in each (10 minute) period it is played for one lucky miner. Miners can improve their odds of winning by investing in computational power. If there are N units of computational power on the network and you own n of them, your expected return is Prob{win}*Reward = (n/N)P_block. Moreover, as I described in a previous post, (and also in my paper with June Ma and Rabee Tourky), the ‘open entry’ aspect means that if each unit of computational power costs c per period, then free entry means that:

Prob{Win per Unit}*Reward = Average Resource Cost per Unit

Because someone is going to win, what this means is that:

Reward = Total Resource Cost of the System

or in this case:

P_block = cN

What Budish adds to this picture is the demand-side of the equation. In particular, while the supply-side leads to lots of computational power being applied to win a block, the benefit of this is supposed to be robustness against some form of attack. For instance, in a “majority attack,” if there are currently N* units of computational power on the network, then by paying cN* + e (where e is a little bit), an attacker can potentially get control of the network. In some situations, a simple majority isn’t enough and you might need AcN* to get control where A (> 1) is a parameter that represents the super-majority you might need to apply your computational power in order to take control for t periods (in expectation).

In this case, you get At.cN* – t.P_block during the t periods of attack. But above we know that P_block = cN, so this equation becomes:

(A – 1)t.P_block > V_attack

Here V_attack is the reward an attacker might get. If the cost of the attack is greater than V_attack, an attack will not occur and the system will be robust.

The big insight is that this is all in terms of flow returns. Why? Because computational power being applied to mining is assumed to be fungible (and so can be easily deployed in and out of the system at will). In addition, during the attack you actually get P_block which lowers the cost of the attack. Once the attack is over, everyone competes as per normal. So Budish notes that Bitcoin is an institution whose long-term viability is based on the potential for very short-term enforcement mechanisms. That is not a good sign.

The above equation is good news in the sense that a higher P_block means that it is less likely an attack will be mounted. However, when we think about a double spending attack, the value of V_attack is related to the value of bitcoins which, of course, is positively related to P_block. So in that sense, the more valuable the transactions, the less robust is Bitcoin. In other words, everything was fine so long as Bitcoin was economically unimportant but as it becomes important there is a problem.

Now, people will note that the ‘best’ chips these days for mining are ASIC chips. These cannot be repurposed for other uses. Hence, the equation Budish identifies may not hold. Indeed, having non-fungible chips makes Bitcoin more robust. Why? To attack you need to invest in ASIC computational power and hence, V_attack must be correspondingly higher to justify that attack. As it becomes hard to find arguments why V_attack would be high without Bitcoin just collapsing, things may be OK.

What is instructive here is that Nakamoto described Bitcoin a democratic like system with “one-CPU-one-vote” which meant that any person could participate. But if it is only robust with specialized chips, that democratic philosophy is undermined. In other words, Bitcoin is only likely to be long-lasting and robust as an institution because technology has subverted the very democratic-style principles that were core to its founding vision.