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homework1 - player’s preferred activity and...

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Nau: Game Theory 1 Updated 8/25/11 Homework 1: 1.1. Here are three possible decision-making techniques for the Battle of the Sexes: Øඏ (a) both players always choose Football. Øඏ (b) each player flips his/her own unbiased coin, and chooses Football if the coin shows heads and Opera if the coin shows tails. Øඏ (c) one of the players flips an unbiased coin, and both players choose Football if the coin shows heads and Opera if the coin shows tails. What will each player’s expected utility be for each of these? 1.2. We can transform the Battle of the Sexes into an equivalent game that is symmetric, by renaming each player’s actions as “give” (i.e., choose the other
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Unformatted text preview: player’s preferred activity) and “take” (i.e., choose one’s own preferred activity). Write the payoff matrix for the transformed game. How does this change affect Problem 1.1? 1.3. Can the above transformation be done on any two-player normal-form game? If so, then tell how. If not, then give a counterexample. 1.4. Assuming that the coins really do produce random results, do the players’ decision-making techniques in Problem 1.1 fit the definition of a mixed strategy? How about Problem 1.2? In each case, explain why or why not....
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