Farmer Jones and Farmer Smith graze their cattle on the same field. If there are 20 cows grazing in the field, each cow produces $4,000 of milk over its lifetime. If there are more cows in the field, then each cow can eat less grass, and its milk production falls. With 30 cows on the field, each produces $3,000 of milk; with 40 cows, each produces $2,000 of milk. Cows cost $1,000 a piece.

(a) Assume that Farmer Jones and Farmer Smith can each purchase either 10 or 20 cows but neither knows how many the other is buying when they make their purchase. Apply game theory in this situation, calculate the payoffs of each outcome and fill in the table below.

(15 marks)

(b) Describe the likely outcome of this game. Describe what would be the best outcome. Explain your answer.

(5 marks)

(c) Does your answer in (b) explain why there used to be more common fields than there are today? Elaborate your answer.

(5 marks)