Problem_Set_2

Problem_Set_2 - credible threats 3 Let v be the outcome...

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OR4350 Introduction to Game Theory Spring 2010 Problem Set #2 Due : Wednesday, February 17, 2010 at noon in the dropbox (on 2 nd floor of Rhodes Hall) Reminder : Write your Section and NetID on the first page of your homework!!! Answers must always include complete explanations/justifications. 1. Binmore, Section 2.12, Number 19. 2. Consider the following game. Initially, Alice picks either Bob or Carol to be her manager. Then her manager chooses which accounting firm to hire. The choices are firms X and Y. Suppose that both Alice and Carol prefer X and Bob prefers Y. (Let’s abbreviate Alice, Bob, and Carol as A, B, and C, respectively.) a. Draw the game tree for this game. b. Find the subgame perfect Nash Equilibrium. c. Write out the strategic form of this game and find all the Nash equilibria. d. Explain how the Nash that are not subgame perfect Nash equilibria do not correspond to reasonable play (hint: this is sometimes called a non-
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Unformatted text preview: credible threats). 3. Let v be the outcome from part (b) in the previous question and let T be the set of outcomes W v ={u: u ≥ A v} (note that one should use the “squiggly” ≥ sign for preferences, but it doesn’t seem to exist in word, so we will use the ordinary ≥ with the proviso that it should be read as “weakly preferred to” meaning, “preferred or indifferent to”.) a. Describe T explicitly. b. Can A force T or can B or C force ~T. c. What does your answer say about extending Zermelo’s theorem (Theorem 2.1 in the text by Binmore) to games with more than 2 players. 4. Binmore, Section 2.12, Number 22. (Note: to say that something is now a Nash Equilibrium with respect to mixed strategies means that when viewing a “best response” that is the best response among all possible mixed strategies.)...
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