Several years ago, President Carter returned from a conference where he pledged to reduce U.S. oil imports to some target level. His advisors were weighing three alternatives to achieve this goal: a tariff of a specified level, a quota of a specified level, and doing nothing. The Saudi's then made threats through "official channels" saying that, depending on the U.S. action, they may retaliate by raising the oil price. The State Department took the Saudi's at their word and sought to determine the best U.S. action if retaliation was a possible Saudi strategy. Skeptics elsewhere pointed out that off-the-record talk is cheap and sought to investigate whether it was "credible" that the Saudi's would adopt a retaliatory strategy. Assume the following information is available to both the Saudi decision-maker and the U.S. decision-maker: U.S. Payoff Saudi Payoff U.S. Action Saudi Action quota retaliate 90 80 quota don't retaliate 100 90 tariff retaliate 75 50 tariff don't retaliate 110 60 nothing retaliate 40 80 nothing don't retaliate 50 100 Assume the U.S. acts first, and the Saudi's observe and then respond to that act. Depict the game tree (extensive form) for this game. Using backwards induction, determine the most likely outcome. Based on your result, discuss if the Saudi threat of retaliation credible (believable)?