There are TWO witnesses, Holly and Buddy, to a crime. Both of them would like to see the perpetrator apprehended. This will happen only if the crime is reported to the police. Since both the witnesses are busy people, each of them would rather have the other person report the crime than reporting it himself or herself. Suppose that the benefit that each of the witnesses get if the criminal is caught is 4 and 0 if not caught. The cost of reporting the crime for each of them is 1.
1. Set up the above scenario with the appropriate payoff matrix, using Report and Not Report as the two strategies. Is there any dominant strategy in this game? Initially, suppose that both witnesses decide simultaneously and independently on whether to report. Find the set of Nash equilibrium.
2. Holly can commit to an action, Report or Not Report, before Buddy. Then Buddy after observing Holly's action has to decide whether to Report or Not Report. Illustrate the game tree and find out the equilibrium outcome using the Rollback method.