Player 1 (a citizen) files taxes honestly (H) or cheats (C). Player 2 (the government) chooses...

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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. 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.

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Analyzing the Tax Evasion Game This game can be analyzed using the concept of Nash Equilibrium where neither player wants to deviate from their chosen strategy given the other players strategy a Optim... View the full answer