Homework7 - Nau Game Theory 3 Updated Homework 7.3 Suppose we have an auction in which the object’s owner colludes with the auctioneer in the

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Nau: Game Theory 1 Updated 11/14/11 Homework 7.1 Here is the payoff matrix for the most commonly used version of the Prisoner’s Dilemma. (a) What is Player 1’s maximin strategy? (b) What is Player 1’s minimax regret strategy? Here is the payoff matrix for the generalized version of the Prisoner’s Dilemma. Recall that the constraints on the numbers are as follows: c > a > d > b 2 a > b + c For each possible combination of a, b, c, and d that satisfies the above constraints, what are (c) Player 1’s maximin strategy? (d) Player 1’s minimax regret strategy? C D C 3, 3 0, 5 D 5, 0 1, 1 C D C a, a b, c D c, b d, d
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Nau: Game Theory 2 Updated 11/14/11 Homework 7.2 In the definition of a Bayesian game, why is the following condition part of the definition? Condition 1 : Ø The games in G have the same number of agents, and the same strategy space (set of possible strategies) for each agent. The only difference is in the payoffs of the strategies.
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Unformatted text preview: Nau: Game Theory 3 Updated 11/14/11 Homework 7.3 Suppose we have an auction in which the object’s owner colludes with the auctioneer in the following fashion: Ø The owner pretends to be one of the bidders, and places bids on the object in an attempt to raise the selling price Ø If the owner’s bid wins the auction, then the object remains the property of the owner (and the owner doesn’t pay the bid) What is the owner’s optimal bidding strategy in each of the following auctions? (a) English auction (b) First-price sealed-bid auction Nau: Game Theory 4 Updated 11/14/11 Homework 7.4 Write the ex ante payoff matrix for the Bayesian game shown here. What is agent 1’s best response to LR? MP ( p = 0.3) L R U 2, 0 0, 2 D 0, 2 2, 0 PD ( p = 0.1) L R U 2, 2 0, 3 D 3, 0 1, 1 StH ( p =0.2) L R U 2, 2 0, 1 D 1, 0 1, 1 Chkn ( p =0.4) L R U 2, 2 1, 3 D 3, 1 0, 0 θ 1,1 θ 1,2 θ 2,1 θ 2,2...
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This note was uploaded on 01/13/2012 for the course CMSC 498T taught by Professor Staff during the Fall '11 term at Maryland.

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Homework7 - Nau Game Theory 3 Updated Homework 7.3 Suppose we have an auction in which the object’s owner colludes with the auctioneer in the

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