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Unformatted text preview: Section 4: Mixed Strategies and Extensive Form Games Daniel Egel September 29, 2008 1 Mixed Strategies As mixed strategies are really important, and I think that they are still a bit unclear to some, I will work through one of the problems on your problem set. However, as you may have noticed, I changed almost everything in the problem very slightly... so dont get any ideas about copying what I do and turn it in as your homework! 1.1 The Setup Following the events of September 11, the United States is increasing its airport security. The inspection game below studies several aspects of the problem. In the game, a Challenger has to decide whether or not to challenge security and Security has to decide whether or not to inspect. (Assume further that all payoffs are Von Neumann-Morgenstern.) The Challengers payoff to challenging and being inspected, t , depends on how good security is. Suppose that an effort to challenge security will be detected with probability d if security decides to inspect. If the challenge is detected, the Challengers payoff to being caught is- 9. If the challenge is not detected, the Challengers payoff is the same as it is if there is no inspection, i.e., the Challengers payoff is a . Potential Smuggler Challenge ( C ) Not Challenge ( NC ) Security Inspect ( I )- 5 ,t 1 , 3 Not Inspect ( NI )- 17 ,a 5 , 2 1.2 The Questions In parts (a)-(e), assume that the payoff to a successful challenge is 12, i.e., a=12.In parts (a)-(e), assume that the payoff to a successful challenge is 12, i....
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- Fall '10