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Findind Equilibrium for Strategic Game

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The manager of a corporate division faces the possibility of an audit every year. She prefers to spend time preparing if she will be audited; otherwise, she would prefer to invest her time elsewhere. The auditor, who gets recognized for uncovering problems, prefers to audit unprepared clients.

If the players match their actions (i.e., the manager prepares and the auditor audits, or the manager doesn't prepare and the auditor doesn't audit), the manager wins with a payoff of 20, and the auditor loses with a payoff of -20. It the actions don't match, the auditor wins with a payoff of 20, and the manager loses with a payoff of -20.

Diagram this game, and comment on the equilibrium.

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Solution Preview

Please refer attached file for better clarity of tables.

Based upon the information given following payoff matrix can be made.

Payoff Matrix

Prepare Does not Prepare
Auditor Audits (-20, +20) (+20, -20)
does not Audit (+20, -20) (-20, +20)

Note: The first figure in the payoff belongs to the Auditor and second figure to the Manager.
Let us analyze auditor's best action in response to each of manager's actions.
If manager decides to prepare: Auditor's best action is ...

Solution Summary

Solution describes the steps and methodology to find out equilibrium for given game theory problem.