The manager of a corporate division faces the possibility of an audit every year

Question

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. If 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.

Explanation / Answer

Draw the squares These will be the four squares prepare Don't Audit(-20,20)(20,-20) Don't(20,-20)(-20,20) There is no dominant strategy by either player. The equilibrium will be a mixed nash. If either player randomizes their selection of action by going 50% one way or 50% the other they make the other player indifferent to their choice of action.

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