Our colleague Ed Felten proposes a hybrid strategy called fairweather mining, where the core idea is that a miner will maintain a presence on both the selfish mining team and the honest team. When the selfish mining team has no lead, the miner switches to the honest team to reap rewards on that side. When the selfish mining team is ahead, he switches back to selfish mining. Felten conjectures that fairweather mining would lead to an unstable situation, where all the selfish miners dissipate as soon as they are behind, and uses this to argue that selfish mining pools would be very short lived.
But Felten's analysis does not account for the proofs of work that miners have to present to collect their amortized payoffs. He seems to be assuming that the miners are compensated at the time they discover a block, and that those earnings are blindly distributed to the members of the pool that were present at the time the block is discovered. This is not how pools operate.
Earnings need to be distributed to pool participants in proportion to the effort they contributed, such that someone with a big FPGA rig that spent a lot of time in the pool will make more money than someone with a puny CPU who spent a tiny amount of time. The pool manager cannot tell who has what kind of equipment at home or wherever else they get their cheap electricity and cooling. And she can't very well ask the participants to self-declare because they would all lie and claim to have huge mining rigs. Instead, pool operators ask participants to furnish proofs of work, that is, solutions to simple cryptopuzzles that they discover by accident on their way to solving the hard cryptopuzzle, kind of like the easy sudokus one might solve on a lazy Sunday while trying to work on a hard one. The number of such puzzles one solves indicates how much time they spent on the sudoku, even if they never get to solve the hard one.
Once the proofs of work are taken into account, we believe that the fairweather strategy falls apart.
To be sure, Felten brings up a critical point. While we have shown that selfish mining dominates is better than honest mining when everybody else follows the honest Bitcoin protocol, we have not shown that it is the dominant strategy for the Bitcoin game. There may be other strategies that actually outperform ours, but fairweather mining is not one of them, at least, not based on the reasoning Felten has provided so far.
On a completely unrelated note, all this talk about mining and dominant strategies bring to mind Program #7 . Back in the day, the Soviets developed techniques for, shall we say, "efficient" mining: namely, they used atom bombs to open up enormous strip mines. That, if anything, is a dominant mining strategy.
We are grateful to Ed Felten for pointing out the need for a clarification involving the use of the word dominates.