Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 25

Suppose the Tragedy of the Commons involved three shepherds (A, B, and C). Suppose the benefit per sheep is 120 -s A - s B - s C , implying that, for example, A's total benefit is s A (120 - s A - s B - s C ) and marginal benefit is 120 - 2s A -s b - s c.
1. Solve the three equations that come from equating each of the three shepherds' marginal benefit of a sheep to the marginal cost (zero) to find the Nash quilibrium.
2. Compare the total number of sheep on the common with three shepherds to that with two.