Player 1 (a citizen) files taxes honestly (H) or cheats (C). Player 2 (the government) chooses how much effort a [0, 1] to invest in auditing Player 1. The players choose simultaneously. If Player 1 chooses H, then her payoff is 0 and Player 2's payoff is 100a. If Player 1 chooses C, then she is caught with probability a (recall that a is Player 2's audit effort). If Player 1 is caught, then her payoff is 100 and Player 2's payoff is 100 100a. If Player 1 is not caught, then her payoff is 50 and Player 2's payoff is - 100a. a.) If Player 2 believes that Player 1 chooses H, what is her optimal level of a? b.) * If Player 2 believes that Player 1 chooses H with probability p, what is her optimal level of a as a function of p? * c.) What is Player 1's best-response function, as a function of a? d.) * Prove that this game does not have a pure-strategy Nash equilibrium. e.) There is a Nash equilibrium of this game in which Player 1 chooses H with probability p = (0, 1) and Player 2 chooses audit effort a. Find the equilibrium values of p and a.