Person A sells their coin to Person B for $1,000. A is $1,000 richer and B is $1,000 poorer.
B sells the bitcoin to C for $2,000. A is still $1k richer, B is $1k richer, and C is $2k in the hole.
C sells to D for $3k. A, B, and C are all $1k richer, but D is out $3k.
At no point in the chain is any actual value created or destroyed; it merely changes hands. So even though the price keeps going up, the total value across all participants never goes up. The sum of the gains and losses of all participants is $0.
(Note that I'm using "$" to represent a generic indicator of value. Feel free to substitute € or ¥ or gold or shares of Facebook stock or whatever.)
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There are two simplifying assumptions above, both of which make Bitcoin not exactly zero sum.
Good news first. Bitcoin can and does create some value in the same way that other currencies do: by facilitating mutually beneficial exchanges of goods and services. Commercial use appears to only be a tiny fraction of all Bitcoin transactions (and an even smaller fraction that wouldn't have been facilitated anyway using some other means of exchange), but it does happen so credit where credit's due.
The bad news, though, is that all of the above requires electricity. A lot of electricity, as it turns out. Both the initial mining and every transaction thereafter require someone, somewhere to burn some amount of power in order to generate proof of work. Since proof of work is explicitly designed to be useless, all that spent power is essentially deadweight loss.
I haven't seen any good numbers on the first recently (and I would love to have my assumptions proven wrong), but given the ginormous estimates of electricity consumed by the second I have a hard time believing the network as a whole isn't substantially worse than zero sum.
It's pretty strange to see people so consumed with it. It reminds me of beanie babies, and my horrible step-grandmother who would send me in to buy them once she had hit her limit. She was an awful speculator and probably has a worthless collection today for all the money she spent on ebay back then. She'd drive to Vegas to buy them, neighboring towns, all over the place. Totally consumed by speculation gambling. It sickens a person to see someone so...lost in that temptation. I'm not sure how else to put it.
Agreed, I've yet to see an ICO that seemed legit.
When you say that the net value is negative even if the network itself has some positive benefit, what is the negative component there? The only negative component of all that electricity usage is externalities, which apply equally to each unit of energy regardless of what it is used for. Pricing externalities into the cost of electricity is obviously something I approve of, but that’s a separate issue, and I doubt the externalities of electricity usage are anywhere near the magnitude of the positive impact of bitcoin.
Incidentally, this is (as far as I understand) where most of the transaction fees ultimately end up. They're paid out to the miner who actually commits a transaction. Mining's a relatively competitive field so people aren't going to be able to charge much of a premium. The miners then have to turn around and use those fees to cover their costs, which in practice means their hardware costs and their electrical bills.