(8 points) A taxpayer (of a particular profile) can either comply with the IRS code, or cheat and receive some benefit. The IRS can either audit the taxpayer at a cost or do nothing. If the taxpayer...

 (8 points) A taxpayer (of a particular profile) can either comply with the IRS code, or
cheat and receive some benefit. The IRS can either audit the taxpayer at a cost or do
nothing. If the taxpayer cheats and the IRS audits then the tax payer faces penalty (fine
plus possibly jail time) and the IRS receives the fine. The payoff matrix:
IRS
Audit (q) Not Audit (1-q)
Cheat (p) -50000, 4000 1000, 0
Tax Payer
Comply (1-p) -500, -300 0, 0
Assume the tax payer cheats with probability p and complies with probability 1 − p, and
IRS audits with probability q and does not audit with probability 1 − q. Find the mixed
strategy Nash equilibrium. Express probabilities in percentage forms and keep two digits
after the decimal point, for example p = 2.34%.

Extracted text: 3. (8 points) A taxpayer (of a particular profile) can either comply with the IRS code, or cheat and receive some benefit. The IRS can either audit the taxpayer at a cost or do nothing. If the taxpayer cheats and the IRS audits then the tax payer faces penalty (fine plus possibly jail time) and the IRS receives the fine. The payoff matrix: IRS Audit (q) -50000, 4000 Not Audit (1-q) 1000, 0 Cheat (p) Tax Payer Comply (1-p) -500, -300 0,0 Assume the tax payer cheats with probability p and complies with probability 1 – p, and IRS audits with probability q and does not audit with probability 1 – q. Find the mixed strategy Nash equilibrium. Express probabilities in percentage forms and keep two digits after the decimal point, for example p = 2.34%.