Question 2 [25%] Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a

of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 106 minutes. Everyone wishes to minimize his/her commuting time. Your tasks: 1 a. [12%] Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied. b. [6%] What is the traffic pattern (strategies) minimizing the total travel time of all commuters (the sum of their travel times)? Describe the corresponding profile of commuting times (individual payoffs/cost). c. [7% ] What does this mean about the Price of Anarchy of this game (assuming that the objective function is the total travel time)? No coding is required.