I'm not sure about question b). I know I have to use mixed strategies I just don't know how to go about it. Also not sure how to answer c).

3. Consider the following game between a tax payer and the government. Suppose the taxpayer earned $10 in year 2005. Tax payer is trying to decide whether to report his true inc0me $10, or lie and report $0 on his tax return. After the government receives the tax return, the government must decide whether to audit the tax payer or not. Of course, when the government is making this decision, it does not yet know whether the tax payer has led truthfully or not. If the tax payer reports $10, he must pay tax $T, where 0