Question

You have to solve the 7th question

Exercises p one of the two doors not selected by the contestant. In opening up a oor, a rule of the show is that Monty is prohibited from opening the door ith the good prize. After Monty opens a door, the contestant is then given he opportunity to continue with the door originally selected or switch to he other unopened door. After the contestant's decision, the remaining two doors are opened. a. Write down an extensive form game of Let's Make a Deal up to (but not including) the stage at which the contestant decides whether to main- tain his original choice or switch to the other unopened door. Thus, you are to write down the extensive form for when (1) Monty Hall chooses the door behind which the good prize is placed; (2) the contestant chooses a door; and (3) Monty Hall chooses a door to open. You may exclude payoffs. b. For the stage at which the contestant decides whether or not to switch, write down the contestant's collection of information sets. In doing so, denote a node by a triple, such as 3/2/1, which describes the sequence of play leading up to that node. 3/2/1 would mean that Monty Hall put the good prize behind door 3, the contestant initially selected door 2, and Monty Hall opened door 1. 7. For the Iraq War game in Figure 2.11, write down the strategy sets for the three players. 8. Derive the corresponding strategic form for the extensive form game in the figure below.

Answer 1

7. In the above diagram, there are three players. They're : Iraq, US and UN. The Iraq has three information sets and Iraq's strategy is a triple of actions. Those are - a) initial code set, b) No WMD set and UN requested inspections and c) WMD set and UN requested inspections. At the information sets, one side it has two actions and the other side it has three actions. The sum total of Iraq strategies are 12.

The other player, US has four information sets. In the first information set a) the UN didn't request inspections, b) in the other, the UN requested inspections and Iraq rejected that request , c) the UN again requested inspections and Iraq has agreed to the request & Weapons of Mass Destruction [WMD] were not found , d) in the last information set the WMD were found and hence the Iraq acquiesced to UN requested inspections. The last information set is considered as a unit set. Hence, the US strategies are four tuple of actions. Each of its four information sets contains two feasible actions such as attacking or not attacking Iraq. The total number of US strategies are 16.

The remaining player, UN has one information set and it contains two nodes corresponding to having WMD or not having WMD of Iraq. The UN strategy set indicates request inspections or not.