(17 Points) 100 monks in a monastery decide simultaneously whether to take a Vow of Silence (V) or not (NV). They would all like to appear pious, but they also do not enjoy not talking at all. Additionally, they appear more pious if they take the vow and few other monks do, and less pious if they don't take the vow and many other monks do. Let in be the number of monks taking the vow of silence. The payoffs for taking the vow (V) and not taking the vow (NV) are given below: U{V)=100m U (N V) = 200 4m (a.) Verify that there is no Nash Equilibrium for 2 5 m 5 99 (in other words, that there is no Nash equilibrium where some monks choose V and some monks choose NV). (b.) Find all Pure Strategy Nash Equilibria of the game. (c.} Are the Nash Equilibria you found in part (b.) Pareto efcient? Explain