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...

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 uses route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time.

Your tasks:

1. 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.


2. 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).


3. What does this mean about the Price of Anarchy of this game (assuming that the objective function is the total travel time)?