12. A businessperson has the choice of either not cheating on his income tax or cheating and making $1000 if not audited. If caught cheating, he will pay a fine of $2000 in addition to the $1000 he owes. He feels good if he does not cheat and is not audited (worth $100). If he does not cheat and is audited, he evaluates this outcome as -$100 (for the lost day). Viewing the game as a two-person zero-sum game between the businessperson and the tax agency, what are the optimal mixed strategies for each player and the value of the game?