At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,15]. The manager of these 20 employees announces that she will contribute d dollars for every dollar that an employee contributes.

The payoff to employee i who makes contribution of x_i dollars is

b_i (1 + d) x_i -x_i, where b_i > 0

Assume that d = 2, b_i = 0.5 for i = 1,2,....,10 and b_i = 0.25 for i = 11, 12....., 20

Considering this, answer the following:

a) What is the best contribution level for any employee i for i = 1,2,....,10?

b) What is the best contribution level for any employee i for i = 11,12,....,20?

c) What is the total contribution level in the Nash Equilibrium by the 20 employees (that is, excluding the contribution by the manager)?

d) What is the contribution level of the manager in the Nash Equilibrium?