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Consider a game between a tax collector (player 1) and a tax payer (player 2).  Player2 has an income of 200 and may eit...

Consider a game between a tax collector (player 1) and a tax payer (player 2).  Player2 has an income of 200 and may either report his income truthfully or lie.  If he reports truthfully, he pays 100 to player 1 and keeps the rest.  If player 2 lies and player 1 does not audit, then player 2 keeps all his income.  If player 2 lies and player 1 audits then player 2 gives all his income to player 1. The cost to player 1 of conducting an audit is 20.  Suppose that both parties move simultaneously (i.e.  player 1 must decide whether to audit before he knows player 2’s reported income).  Find the mixed-strategy Nash equilibrium for this game and the equilibrium payoffs to each player.  Explain in your own words the meaning of these results.

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Payoff table: Player II Strategy Таx рayer Player I Strategy Tax collector Probability Truthful Lie Audit 100 X2=200 No auditMaximin Decision Criterion to the strategies for Player I Minimum value of Audit strategy: Мa3тin (r,, г.) — 100 Minimum vaNo audit 1-P1 3=100 0=x Probability 1-P2 Р2 Maximum of these two minimum values Оp, 3D max (Mд, MNA) — 100 Minimax Decision CPayoff Table with Minimax Criterion of Player II Player II Strategy Tax payer Player I Strategy Tax collector Probability TruPayoff Table with combined strategies of Player I and II Player II Strategy Tax payer Player I Strategy Tax collector ProbabiPayoff table: Player II Strategy Tax payer Player I Strategy Tax collector Probability Truthful Lie Audit 100 X2 200 P1 1-P NExpected Gain for player I: Probability of choosing strategy Audit: Probability of choosing strategy No audit: 1-Р1 If PlIf Player I is same if player II selects strategy Truthful or Lie,we equate the expected gain from each of these strategies:Repeat this process for Player II to find out his mixed strategy The expected loss for Player II, for being Truthful 100-р2 +There is a simultaneous gain of 100 for player I and loss of 100 for player II, so the mixed strategy of the two players has

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