solve B(iv)

5) Consider the following scenario. There are N witnesses to a crime. Each witness can report or not report the crime, and they act simultaneously. The payoff to each witness is gif another witness reports the crime 9-c if he/she reports the crime 0 if nobody reports the crime That is, each witness wants the crime to be reported and benefits from it being reported, but there is a personal cost to reporting. Assume that 9>c>0 (a) Construct a pure strategy NE of the game in which the crime is reported with prob- ability one. How many witnesses report the crime? (15 POINTS) (b) Now consider a symmetric mixed strategy NE of the game in which each witness does not report the crime with probability p, and reports with probability 1-P. (i) What is the probability with which nobody reports the crime? (HINT: Each individual does not report with probability p. Given this, what's the probability everyone ends up not reporting?) (5 POINTS) (ii) Solve for the equilibrium probability p by writing down the indifference condition of each witness. (10 POINTS) (iii) What happens to each person's probability of not reporting as the number of witnesses increases to infinity (N goes to oo)? Does it increase or decrease, and what does it converge to? (5 POINTS) (iv) What happens to the probability that nobody reports the crime as the number of witnesses increases to infinity? Does it increase or decrease and what does it converge to? (15 POINTS)