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Game Theory
5. Suppose that a person owes $100 in taxes to the government. The person can either pay the $100 or cheat and pay nothing. The government can either audit this person or not audit him/her; the decision about whether to audit is made without knowing what choice the person made. If the government audits a person who picked Cheat, the tax evasion is discovered and the person must pay $150 to cover both his/her taxes and a fine imposed on detected cheaters. Auditing is costly; when the government audits a person, both the government and the person lose $10 (this cost must be paid regardless of whether the person chose Cheat or Pay).
a. Write the above game in normal form.
b. Determine whether there is an equilibrium in pure strategies in this game.
c. Suppose that the government chooses Audit with probability p. Determine the value at which p must be set to ensure that the person gets the same expected payoff from Cheat as he gets from Pay (this is equivalent to asking you to find the value of p that holds in a mixed strategy equilibrium in this game).
d. Suppose that the person feels somewhat guilty when he chooses Cheat. We will represent this feeling of guilt by saying that the person’s payoff when he chooses Cheat (regardless whether he is audited or not) falls by 20. In this case, at which value must p be set to ensure that the person gests the same expected payoff from Cheat as he gets from Pay?
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