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.