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

Assume that Farmer Singh and Farmer Vu can each purchase either $10$ or $20$ cows, but that neither knows how many the other is buying when she makes her purchase. Use the table to show the payoffs of each outcome.

$\backslash$table$[[\backslash$table$[[$Vu$\text{'}$s$],[$Decision$]],$Singh's Decision$],[,10$ cows,,,$20$ cows$],[10$ cows,Results: $$40,000$grad,profit for Singh, and,profit for Vu$.,$Results:,profit for Singh, and$],[20$ cows,Results:,profit for Singh, and,profit for vu$.,$Results:,$\_$ profit for Singh, and$]]$