Juan Beccuti, Christian Jaag (Swiss Economics Working Paper 0060)
Consider a game in which Bitcoin miners compete for a reward of each solved puzzle in a sequence of them.
model it as a sequential game with imperfect information, in which miners have to choose whether or not to report their success.
Show that the game has a multiplicity of equilibria and we analyze the parameter constellations for each of them.
In particular, the minimum requirement to find it optimal not to report is decreasing with the number of miners who are not reporting, and increasing the heterogeneity among players reduces the likelihood that they choose not to report
Ayelet Sapirshtein, Yonatan Sompolinsky, and Aviv Zohar (The Hebrew University of Jerusalem)
From Stubborn Mining paper,
Concurrent to and independent of our work, Sapirshtein et al. also observe that selfish mining is suboptimal. They define a broad strategy space and use a combination of analytic bounds and numeric solvers to compute approximately-optimal strategies from this space. Their strategy space is a generalization of our stubborn mining strategies; however, they do not consider how to compose mining attacks with eclipse attack
Fault tolerance in uncoordinated majority model: ~0.2321
In our model where the adversary can control the delivery of messages, the bitcoin protocol is not incentive compatible even for players controlling less than a 1/3 of the computational resources—there is a selfish mining attack which enables an attacker to gain 1/2 of the block rewards
Define and analyze 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.