Experience with Bitcoin shows that the largest pools are often open, allowing anyone to join. It has long been known that a member can sabotage an open pool by seemingly joining it but never sharing its proofs of work. The pool shares its revenue with the attacker, and so each of its participants earns less. So what is the miner’s dilemma?

The authors of this paper define and analyse a game where pools use some of their participants to infiltrate other pools and perform such
an attack. With any number of pools, no-pool-attacks is not a Nash equilibrium.

With two pools, or any number of identical pools, there exists an equilibrium that constitutes a tragedy of the commons where the pools attack one another and all earn less than they would have if none had attacked.

For two pools, the decision whether or not to attack is the miner’s dilemma, an instance of the iterative prisoner’s dilemma. The game is played daily by the active Bitcoin pools, which apparently choose not to attack. If this balance breaks, the revenue of open pools might diminish, making them unattractive to participants.

To find out more about this game and the results that are on offer, download this whitepaper.