The Internal Revenue Service (IRS) must decide whether to audit a certain tax return to discover whether it is accurate or not. Suppose that the IRS and the tax payer simultaneously choose whether to audit (A) or not (NA) and cheat (C) or not (NC), respectively. The true amount the tax payer owes the IRS is 1. He either reports the true amount or cheats and reports 0. If the IRS audits the tax return the truth is always discovered and 1 is collected. Auditing costs c, where c < 1, and if the tax payer is caught cheating, a fine of amount f > 0 is collected from the tax payer. The goal of the IRS is to maximize expected revenues (i.e., tax collection minus auditing costs, if any, plus fines, if any) whereas the taxpayer wants to minimize expected payments (i.e., tax payment minus fines, if any).

(a) Draw a 22 payoff matrix for this interaction, clearly labelling the players, their strategies, and the payoffs.

(b) Find all the (pure or mixed strategy) Nash equilibria.