Sadaam Hussein is deciding where to hide his weapons of mass destruction (WMD), while the United Nations is deciding where to look for them. The payoff to Hussein from successfully hiding the WMD is 5 and from having them found is 2. For the UN, the payoff to finding the WMD is 9 and from not finding them is 4. Hussein can hide them facility X, Y, or Z. The UN inspection team has to decide which facilities to check. Because the inspectors are limited in terms of time and personnel, they cannot check all facilities.

a. Suppose the UN has two pure strategies: It can either inspect facilities X and Y (both of which are geographically close to each other) or inspect facility Z. Find a Nash equilibrium in mixed strategies.

b. Suppose the UN can inspect any two facilities, so that it has three pure strategies. The UN can inspect X and Y, X and Z, or Y and Z. Find a Nash equilibrium in mixed strategies.