# Determining Dominant Strategy Equilibrium in Two Player Game

1. Two airlines, A and B, are deciding to choose whether Atlanta or Chicago should be their major hub. Given the diagram here, find all equilibira of this game.

A

Atlanta Chicago

B Atlanta $40m,$40m $85m,$60m

Chicago $60m,$85m $35m,$35m

2. 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 else where. 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 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.

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#### Solution Preview

1. Whenever you have a game matrix given as above there is a very simple way to determine the dominant-strategy equilibrium. Consider airline B. They get the first item in each cell as the payoff. They have an option of either choosing Atlanta or choosing Chicago. If they assume that airline A is choosing Atlanta, then they are better off choosing Chicago, since they will have a payoff of 60 instead of 40. Similarly, they are better of choosing Atlanta if they believe that airline A is choosing Chicago. In such a case their payoff is 85 instead of 35.

Underline these payoffs in the diagram.

A similar analysis of ...