Jones TV and Smith TV are the only two stores in your town that sell flat panel TV sets. First, Jones will choose whether to charge high prices or low prices. Smith will see Jones’s decision and then choose high or low prices. If they both choose High, each earns $10,000. If they both choose Low, each earns $8,000. If one chooses High and the other chooses Low, the one that chose High earns $6,000 and the one that chose Low earns $14,000.
a. Draw the game tree. Use backward induction to solve this game.
b. Suppose Smith goes to Jones and promises to choose High if Jones chooses High. Is this a credible promise?
c. Now suppose Jones starts a new policy that says it will always match or beat Smith’s price. It advertises the new policy heavily and so must choose Low if Smith chooses Low. So the game now has the following structure. First, Jones chooses High or Low. Second, Smith chooses High or Low. Third, if Jones has chosen High and Smith has chosen Low, Jones meets Smith’s price and chooses Low. Draw the game tree. Use backward induction to solve this game.