2. There are two routes from Round Rock to Dallas, and a continuum of individuals represented by the interval [0, 1], who need to make this trip. If a fraction of the individuals use route A and 1-2 fraction use route B, the travel times are c(A,x)=x². c(B, x) = 1-x. Solve for a Nash equilibrium, æ*. Write down total travel time as a function of z, W(z). How does W(z) vary as we increase a slightly above z*? What value of z minimizes W(x)?.

2. There are two routes from Round Rock to Dallas, and a continuum of individuals represented by the interval [0, 1], who need to make this trip. If a fraction of the individuals use route A and 1-2 fraction use route B, the travel times are c(A,x)=x². c(B, x) = 1-x. Solve for a Nash equilibrium, æ. Write down total travel time as a function of z, W(z). How does W(z) vary as we increase a slightly above z? What value of z minimizes W(x)?.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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