It is often asserted (for example, in the Bitcoin white paper [22]) that a cartel can double-spend Bitcoins. In a strict sense, this is true: a cartel can spend a Bitcoin by paying it to a player Alice, receiving goods or services, and then shifting the consensus choice of history to a branch where that coin is instead paid to a different player Bob. However, we argue that double-spending by a cartel has a limited payoff. Bitcoins have value because people are willing to trade them for goods and services. If players were unwilling to accept Bitcoins for trade or unwilling to spend Bitcoins for fear of having their payments nullified, the value of Bitcoins would diminish significantly as players lost confidence in the system. Worse, because players are encouraged to generate a new identity for each transaction and because identities are not linked to any side information, players cannot easily determine whether a proffered payment is coming from the double-spending cartel or an honest user. Thus, a rational player should refuse to accept any payments when there is a significant threat of double-spending.
As a cartel must outmine the entire Bitcoin network and thus outspend the entire Bitcoin network for as long as it would remain a cartel, we believe it is very unlikely that a cartel could double-spend enough to recover the cost of the attack...
As described above, a 51% cartel attack is unlikely to generate enough reward within the Bitcoin economy to be worthwhile to the attacker. However, this does not rule out the possibility of a 51% attack that aims to destroy the Bitcoin economy in order to achieve utility outside the Bitcoin economy. We call this the Goldfinger attack after the character in film who tries to undermine U.S. currency by ruining its gold backing [15]...
In all of these cases, the attacker must achieve enough utility to justify the substantial cost of an attack. We agree with Becker et al. that it is unlikely that a protest movement could muster the resources to launch a successful attack. And at present it does not appear possible to acquire a short position on Bitcoins that is large enough to justify an attack. (2013)
The Economics of Bitcoin Mining, or Bitcoin in the Presence of Adversaries
Joshua A. Kroll, Ian C. Davey, and Edward W. Felten,
Princeton University
https://www.econinfosec.org/archive/weis2013/papers/KrollDav...