Generalized Tipping Model

Recall the generalized tipping model discussed in the exercise of Section 7. We assumed 𝑏 − 𝛾 > 1 in the lecture note, but now assume 𝑏 − 𝛾 < 1.

(a) (5 points) Is there equilibrium where no one participate the protest? State yes or no explicitly. Explain the reason.

(b) (5 points) Suppose that all players make a decision independently and simultaneously. Is there any equilibrium where 𝑛 players participate depending on the parameter values even with 𝑏 − 𝛾 < 1? State yes or no explicitly. If yes, show the condition on the parameter values for an existence of such equilibrium, and explain the reason. If no, explain the reason.

*The attached picture is the generalized tipping model discussed in the exercise of Section 7.