Econ171_H1 - Econ 171 Introduction to Game Theory Homework...

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Homework Problems #1 These problems are intended to supplement the in-class lectures (as well as give you exposure to the types of problems you will see on the midterms and ±nal exams). They will not be collected or graded. However, it is very di¢ cult to learn game theory without working problems. Therefore, I strongly encourage you to work through them. 1. Static Games: Consider the following 3x3 game. Player 2 West Midwest East West -2, 3 -3, 1 -2, 2 Player 1 Midwest 2, 4 -2, 4 -2, -1 East 0, -1 0, -1 0, 0 (a) Name the strategies that are eliminated by Iterated Elimination of Strictly Dom- inated Strategies. (b) Find all Pure-Strategy Nash Equilibria. (c) Find any Mixed-Strategy Nash Equilibria. 2. Static Games: Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name shares they would like to have, s 1 and s 2 , where 0 s 1 ; s 2 1 . If s 1 + s 2 1 , then the players receive the shares they named; if s 1 + s 2 > 1 , then both players receive zero. What are the pure strategy Nash Equilibria of this game? 3. Cournot Revisited: price of Widgets will be determined by the total amount of Widgets brought to the P ( Q ) = 100 ± Q , where Q = q 1 + q 2 . Assume cost functions with constant marginal cost, i.e. C 1 ( q 1 ) = C 2 ( q 2 ) = 10 q i for i = 1 ; 2 . In class, we found that the Nash Equilibrium in this game is
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This note was uploaded on 04/06/2010 for the course ECONOMICS Econ 171 taught by Professor Jack during the Spring '10 term at UCSB.

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Econ171_H1 - Econ 171 Introduction to Game Theory Homework...

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