8.4 Two security guards employed by different companies, i = 1, 2, simultaneously choose how many hours li to spend patrolling a street. The average benefit per hour can be expressed as 10−li+

lj 2

and the (opportunity) cost per hour for each is 4.

Security guard i’s average benefit is increasing in the hours guard j spends patrolling his side of the street because the security of the street in general depends on the security of the neighbouring area.
a.
Compute the Nash equilibrium.
b.
c.
Graph the best-response functions and indicate the Nash equilibrium on the graph.
On the graph, show how the equilibrium would change if the intercept of one of the guards average beneit functions fell from 10 to some smaller number.