prel1 - Prelim I OR&IE 4350 Fall 2008 Game Theory Write...

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Unformatted text preview: Prelim I OR&IE 4350 Fall 2008 Game Theory Write answers directly on the exam. Give brief justifications for your answers. Name: Section: I will not give, use, or receive unauthorized aid on this exam. Signed: 1. (40 points: 10, 4, 8, 5, 3, 3, 2, 5) Consider the following game. Three cards, an ace, a king, and a queen, are shuffled and one is dealt to player II . She looks at it (player I can’t see it). If it is the ace, she must say “Ace”; if the King, she can say “Ace” or “King”; if the queen, she says “Ace” or “Queen.” If she says “King,” the game is over and each player gets $0; if “Queen,” player I gets $1 and II loses $1. If player II says “Ace,” player I can either believe her (B), in which case he loses $1 and she gets $1, or challenge her (C), in which case he loses $5 and she gets $2 if she has the ace, and otherwise he gets $2 and she loses $5. Assume both players are risk-neutral and use von Neumann-Morgenstern utility functions with u ($ x ) = x for each. (a) Complete the extensive form of the game given below. Mark nodes and edges as appropriate, with information sets as needed. (If the edges from a node are marked B and C, mark the higher one B (for “believe”).) 2 1-1-5-1 1 A (b) How many pure strategies does each player have? Justify. (c) If AQ denotes “say “Ace” if have King, say “Queen” if have Queen,” etc., com- plete the strategic form of the game below. II AQ 1 B-1 I Explain how you get one of the fractional entries. (d) Find a strongly dominated strategy for one of the players. Are there any Nash equilibria (in pure strategies)? If you were player II , would you occasionally bluff (say “Ace” when you have the king or queen)? Why or why not? (e) Suppose for the remaining parts that player...
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prel1 - Prelim I OR&IE 4350 Fall 2008 Game Theory Write...

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