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Each of 50 commuters (commuting in the same direction) must choose which of two routes to take: Route 7, which is a four-lane highway, or Route 10, which is a two-lane highway. Every commuter cares only about minimizing the expected time spent commuting. If k commuters take Route 7, then each of these k commuters spends 30+ k minutes commuting. If n commuters take Route 10, then each of these n commuters spends 30 + 2n minutes commuting. (a) Find all pure strategy Nash equilibria of the game in which all commuters simultaneously

Each of 50 commuters (commuting in the same direction) must choose which of two routes to take: Route 7, which is a four-lane highway, or Route 10, which is a two-lane highway. Every commuter cares only about minimizing the expected time spent commuting. If k commuters take Route 7, then each of these k commuters spends 30+ k minutes commuting. If n commuters take Route 10, then each of these n commuters spends 30 + 2n minutes commuting. (a) Find all pure strategy Nash equilibria of the game in which all commuters simultaneously

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Each of 50 commuters (commuting in the same direction) must choose which of two routes to take: Route 7, which is a four-lane highway, or Route 10, which is a two-lane highway. Every commuter cares only about minimizing the expected time spent commuting. If k commuters take Route 7, then each of these k commuters spends 30+ k minutes commuting. If n commuters take Route 10, then each of these n commuters spends 30 + 2n minutes commuting. (a) Find all pure strategy Nash equilibria of the game in which all commuters simultaneously choose which route to take. (b) Find all symmetric mixed strategy Nash equilibria of the simultaneous-move game (a Nash equilibrium is symmetric if all players use the same strategy). You may use the fact that if r events each occur with independent probability p, then the expected number of occurrences is rp.
Transcribed Image Text:Each of 50 commuters (commuting in the same direction) must choose which of two routes to take: Route 7, which is a four-lane highway, or Route 10, which is a two-lane highway. Every commuter cares only about minimizing the expected time spent commuting. If k commuters take Route 7, then each of these k commuters spends 30+ k minutes commuting. If n commuters take Route 10, then each of these n commuters spends 30 + 2n minutes commuting. (a) Find all pure strategy Nash equilibria of the game in which all commuters simultaneously choose which route to take. (b) Find all symmetric mixed strategy Nash equilibria of the simultaneous-move game (a Nash equilibrium is symmetric if all players use the same strategy). You may use the fact that if r events each occur with independent probability p, then the expected number of occurrences is rp.
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