Consider the simultaneous move game between a taxpayer and a tax inspector. The taxpayer chooses whether or not to underreport their taxable income. The tax inspector chooses whether or not to audit the income report. The cost of auditing is c > 1 and the fine (including tax payment) imposed if the taxpayer is caught cheating is F (with F > c > 1). With a truthful report the taxpayer has to pay a tax of 1 unit of income. The payoffs are given in the matrix where the first number in each cell denotes the tax inspector’s payoffs and the second number is the taxpayer’s payoffs. Find the Nash equilibria of this game, considering both pure and mixed strategies.
