  Mafia can be described as an experiment in human psychology and mass
hysteria, or as a game between informed minority and uninformed majority. Focus
on a very restricted setting, Mossel et al. [to appear in Ann. Appl. Probab.
Volume 18, Number 2] showed that in the mafia game without detectives, if the
civilians and mafias both adopt the optimal randomized strategy, then the two
groups have comparable probabilities of winning exactly when the total player
size is R and the mafia size is of order Sqrt(R). They also proposed a
conjecture which stated that this phenomenon should be valid in a more
extensive framework. In this paper, we first indicate that the main theorem
given by Mossel et al. [to appear in Ann. Appl. Probab. Volume 18, Number 2]
can not guarantee their conclusion, i.e., the two groups have comparable
winning probabilities when the mafia size is of order Sqrt(R). Then we give a
theorem which validates the correctness of their conclusion. In the last, by
proving the conjecture proposed by Mossel et al. [to appear in Ann. Appl.
Probab. Volume 18, Number 2], we generalize the phenomenon to a more extensive
framework, of which the mafia game without detectives is only a special case.
