Consider the following routing game with two routes where l,12 are the travel times on each...

 

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Consider the following routing game with two routes where l₁,12 are the travel times on each route when the fraction of traffic on each route is given by ₁ and 22. The parameters a, b satisfy a > 0 and 0 ≤ b ≤ 1. See Figure 1. (a) Find the optimal routing [3 pt.] (b) Find the equilibrium routing [3 pt.] (c) Suppose everyone values saving an hour of time at $10/hour. What tax and on which route will result in the optimal routing as an equilibrium? [3 pt.] (d) What is the maximum ratio of inefficiency of the travel time under equilibrium routing relative to the optimal routing ( AvgTime Equi) [1 pt.] AvgTime Opt Consider the following routing game with two routes where l₁,12 are the travel times on each route when the fraction of traffic on each route is given by ₁ and 22. The parameters a, b satisfy a > 0 and 0 ≤ b ≤ 1. See Figure 1. (a) Find the optimal routing [3 pt.] (b) Find the equilibrium routing [3 pt.] (c) Suppose everyone values saving an hour of time at $10/hour. What tax and on which route will result in the optimal routing as an equilibrium? [3 pt.] (d) What is the maximum ratio of inefficiency of the travel time under equilibrium routing relative to the optimal routing ( AvgTime Equi) [1 pt.] AvgTime Opt

Answer rating: 100% (QA)

a The best route is the one that has the shortest amount of time spent traveling which is route 1 b The equilibrium routing is the route that has the shortest travel time which is route 1 because it i... View the full answer