Problem
You are playing a truth or lie game where you submit a truthful or false credit score to your bank in order to get requested money from them. If you tell the truth that requires you to pay a $2000 fee, or you could lie and forge your credit score and gain the requested $2000.
The bank either accepts your credit report as is, or incurs a cost of $1000 to audit the report, which reveals whether it is real or forged. You will be fined $10,000 for submitting a false credit score if it is discovered through an audit and will also have to pay the truthful amount of fees.
If the bank does not audit you, you will pay the fee or receive the requested money according to your report being real or fake. The bank receives fees and the bank pays out any requested money.
A. Write the game in extensive form with explanation.
B. Write the game in strategic form with explanation.
C. Does a pure strategy equilibrium exist? If so, find and interpret the equilibrium. If not, explain why.
D. Does a mixed strategy equilibrium exist? If so, find and interpret it. If not, explain why.