Iran is trying to decide whether it should pursue its nuclear weapons program, and its decision will be affected in large measure by what it expects the United States to do. Your assignment is to use an extended-form game to analyze what Iran may choose to do. Your paper will be evaluated according to how correctly it uses the diagramming techniques we covered in class and how clearly the text of your paper explains the logic of the game. You should present the appropriate extended-form game, with the various moves clearly indicated, probabilities associated with various actions, outcomes and their values as well as appropriate information sets

This is the problem:

Imagine Iran initially believes it is playing against a Tough United States (TUS) with probability q, and against a Nice United States (NUS) with probability (1-q). Iran is contemplating making two moves: "C" would be to continue its nuclear weapons program, leading ultimately to the development of a nuclear-weapons capability; "S" would be to stop developing nuclear weapons immediately. Assume Iran chooses "C" initially.

In response to Iran's move of "C", the United States has two moves available: "D" would be to deploy the 7th Fleet on a long-term basis in the Strait of Hormuz and to engage in war games in the area; "ND" would be to not deploy the 7th fleet and to take no militarily hostile action. Iran believes that the probability that TUS would deploy the 7th Fleet is m, while the probability that NUS would deploy the fleet is m'. m > m'

Assume the United States deploys the 7th Fleet. Iran then has a final choice of "C" or "S", as described above. Should Iran choose "C", the United States has a choice to make: "A" would mean launching a military attack on Iran, halting the development of Iran's nuclear weapons for the time being; "NA" would mean to not attack Iran, allowing them to have nuclear weapons. TUS would choose "A" while NUS would choose "NA". Should Iran choose "S" at this stage, TUS would choose "CC" ("Continue Containment") while NUS would choose "R" ("Reward").

In this last stage there are four possible outcomes: Iran chooses C, the US chooses A; Iran chooses C, the US chooses NA; Iran chooses S the US chooses R; and Iran chooses S and the US chooses CC. The values Iran places on these outcomes are 0, 10, 7 and 2, respectively.

a) Draw the tree that captures the extended-form game described above. Make sure you clearly indicate the moves, probabilities, payoff values, and information sets.