SITUATION: THE IRAQ WAR AND WEAPONS OF MASS DESTRUCTION
Now let’s take on some recent history: the situation faced by Iraq, the United Nations, and the United States that culminated in the U.S. invasion of Iraq on March 20, 2003. At issue is whether Sadaam Hussein has weapons of mass destruction (WMD). As shown in FIGURE 2.10, Iraq is modeled as hav- ing a choice of possessing or not possessing WMD. Without knowledge of Iraq’s choice, the United Nations decides whether to request inspections of Iraq. The United Nations then has one information set, which includes both of Iraq’s feasible actions: the one when it has WMD and the other when it does not. If the United Nations chooses not to request inspections, then the United States decides whether or not to invade Iraq, at which point we’ll consider the game done. If the United Nations does request inspections, then the move goes back to Iraq. If Iraq does not have WMD, then it can choose to deny inspections or allow them. If, instead, Iraq has WMD, then it can deny inspections, allow inspections, or allow inspections and hide the WMD. With the last option, suppose Iraq succeeds in preventing inspectors from finding WMD. Assume that when Iraq does have WMD and does not hide them from the inspectors, the WMD are found. After Iraq moves in response to the request for inspections by the United Nations, and the outcome of the inspections is revealed, the United States moves again regarding whether to attack Iraq.
The United States has four information sets. The information set de- noted I includes the two nodes associated with (1) Iraq having WMD and the United Nations not choosing inspections, and (2) Iraq not having WMD and the United Nations not choosing inspections. Although the United States doesn’t get to observe Iraq’s choice, it does get to observe the UN de-
cision. Information set II corresponds to the scenario in which inspections are requested by the United Nations and allowed by Iraq, but WMD are not found, either be- cause Iraq does not have them or because it does have them but has successfully hidden them from the in- spectors. Information set III denotes the situation in which the United Nations requests inspections, but they are refused by Iraq; once again, the United States doesn’t know whether Iraq has WMD. The lone single- ton information set for the United States is node IV,
which is associated with Iraq’s having WMD, the United Nation’s having re- quested inspections, and Iraq’s having allowing unobstructed inspections, in which case WMD are found. A similar exercise can be conducted to describe the one information set of the United Nations and the three in- formation sets of Iraq (all of which are singletons, as Iraq is the only one hiding something).
Now let us return to the Mugging game and suppose that the mugger not only chooses whether to use a gun and whether to show it, but also whether to load the gun with bullets. If Simon sees the gun, he doesn’t know whether it is loaded. Write down the extensive form of this strategic situation. (You can ignore payoffs.)
2.2 CHECK YOUR UNDERSTANDING
FIGURE 2.10 Iraq War and WMD. The Abbreviations W and NW Represent War and No War, Respectively
II
I II I
IVIVI I II I I
Iraq
Iraq Iraq
Iraq
UN
UN
1
10
11
11
14 5US
US
War No war No war
2
6
10
13
13 6
War No war No warDeny
NO WMD WMD
Allow
Inspect Inspect Do not inspect
Do not inspect
Deny Allow Allow & hide
7
1
12
7
9 1
War
3
5
9
14
12 7
War
5
2
13
8
8 2
W NW
6
3
14
9
10 3
W NW
4
4
8
12
4 11
W NW
US
US
US
33
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