6. There are two routes for driving from A to B. One is a freeway, and the other consists of local roads. The benefit of using the freeway is constant and equal to 1.8, irrespective of the number of people using it. Local roads get congested when too many people use this alternative, but if too few people use it, the few isolated drivers run the risk of becoming victims of crime. Let x represent the fraction of the population using the local roads. The benefit to each driver on the local road is given by 1 + 9x - 10x².

NOTE: You will have to use the quadratic formula to answer question 6.

a. Find the three possible Nash equilibria values of x.

b. Which are stable and which are unstable?

c. Briefly explain.

d. Find the efficient equilibrium (the value of x that maximizes the total benefit to the whole population).