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
Fault count assumptions are not appropriate for public blockchains, because public blockchains exist in an oligopolistic setting, where a very small number of miners or coin holders (or reputation holders, in more exotic architectures) control a vast majority of the weight in the consensus.
1. The cartel cannot hide the fact that the censored validators are missing.
2. The cartel had to be punished whenever validators appeared to be missing.
3. It was therefore also necessary to penalize validators who go offline, because it could not be clear to the protocol whether they were being censored, or whether they were offline of their own accord.