[cryptography] Bitcoin observation

Jon Callas jon at callas.org
Tue Jul 5 02:44:57 EDT 2011

I was sitting around the other weekend with some friends and we were talking about Bitcoin, and gossiping furiously about it. While we were doing so, an interesting property came up.

Did you know that if a Bitcoin is destroyed, then the value of all the other Bitcoins goes up slightly? That's incredible. It's amazing and leads to some emergent properties.

If you have a bunch of Bitcoins and you want to increase your worth, you can do this by one of three ways:

(1) Create more Bitcoins.
(2) Buy up more Bitcoins, with the end state of that strategy being that you've cornered the market.
(3) Destroy other people's Bitcoins. The end state of that is also that you've cornered the market.

I also observe that if the player succeeds at either strategy (2) or (3), then Bitcoins are no longer a decentralized currency. They're a centralized currency. (And presumably, that player wins the Bitcoin Game.)

I'll go further and note that if a self-stable oligarchy manages to buy or destroy all the other  Bitcoins, they win as a group, too. With enough value in the Bitcoin universe, and properly motivated players, that could easily happen.

I wonder myself when it is more efficient to destroy a Bitcoin than buy or create one? Let's call the value of the energy to create one C. We'll call the value to buy one B. There must be some constant H where H*C or H*B makes it as efficient to destroy one than to buy or create. I suppose there's really two separate constants, H_c and H_b.

Nonetheless, I call this H because it's the Highlander Constant. You know -- there can only be one! If H is large enough, then you have unrestricted economic war that leads to a stable end where a single player or an oligarchy holds all the bitcoins.

So if we consider a universe of N total coins and a total market value of V, and a players purse size of P coins, what's the value of H? I think it's an interesting question.

I have some other related things to muse over as well, like what it means to destroy a bitcoin. If you silently destroy one, the value of the remaining coins increases passively through deflation. But if you publicly destroy one, you could see an immediate uptick. Does revealing the value of a coin destroy it? Do you need to publicly destroy one through some zero-knowledge proof? 

Also, does public destruction actually hurt the market by making people tend to not want to put money into Bitcoins? Might this form some sort of negative feedback on the value of H, by cheapening Bitcoins as a whole? But is there a double-negative feedback through the fact that if people want to sell coins cheaply, the big players just buy them cheap and run the market back up that way?

The end of all this musing, though, is that I believe that a decentralized coinage that has the property that destroying a coin has value *inevitably* leads to centralization through the Highlander Constant.



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