# HW2 - Econ 398 Homework 2 Due 1 Four players Alice Bertha...

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Econ 398 Homework 2 Due Jan 30, 2009 1. Four players, Alice, Bertha, Cora, and Delores are put into separate rooms so they cannot communicate with one another. They have to write either “\$3” or “\$10” on a piece of paper, and then the papers are collected. If at least one of the four wrote “\$3”, then all four get what they wrote on their paper. If every player wrote “\$10”, then no player gets any money. What strategy profiles are Nash equilibria? Explain why those strategy profiles are Nash equilibria, and why other strategy profiles are not Nash equilibria. 2. Dixit & Skeath, Chapter 4, problem number 6. 3. Two animals are fighting over some prey. Each can be “passive” or “aggressive”. Each prefers to be “aggressive” if its opponent is “passive”, and each prefers to be “passive” if its
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Unformatted text preview: opponent is “aggressive”. Given its own stance, it prefers the outcome in which its opponent is “passive” to that in which its opponent is “aggressive”. This situation is called the Hawk-Dove game. Draw the game bi-matrix and find the Nash equilibria. 4. In the following game, find the Nash equilibria. For each Nash equilibrium, state whether it is Pareto efficient or inefficient. If the equilibrium is Pareto inefficient, give a strategy profile that is a Pareto improvement. Player 2 L1 L2 R1 R2 Player 1 T1 1 , -1 7 , 8 12 , 1 5 , 2 T2 5 , 5 2 , 6 10 , 9 6 , 11 B1 -3 , 2 2 , 8 12 , 9 0 , 12 B2 4 , 12 7 , 11 14 , 2 3 , 4 5. Dixit & Skeath, Chapter 4, problem 10....
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