Question: You own two companies Uno and Due. At the end of a fiscal year, Uno should have a tax bill of $3 million and Due should have a tax bill of $1 million. By cooking the books you can file tax returns making it look as though you should not have to pay any tax at all for either Uno or Due, or both. Due to limited resources, the IRS can only audit one company. If a company with cooked books is audited, the fraud is revealed and all unpaid taxes will be levied plus a penalty of p% of the tax due.
(a) Set this up as a matrix game. Your payoffs will depend on p.
(b) In the case the fine is p = 50%, what strategy should you adopt to minimize your expected tax bill?
(c) For what values of p is complete honesty optimal?