Chapter 12: Game Theory: Fun Only if You Win business situations, if you move first, your rival may be able to neutralize your decision by moving second. You need to develop a decision-making rule that helps you anticipate your rival’s decision. Decision-makers use backward induction in sequential games. Backward induction means that you develop your decision by looking at the future, or at how the game ends. Consider the decision tree in Figure 12-4. Two car dealers, Cathy’s Cars and Otto’s Autos, must decide whether to raise, lower, or charge the same price on their used cars. Because of her leadership position in the market, Cathy’s Cars chooses her used car price first, and then Otto’s Autos follows. When establishing her price, Cathy needs to consider how Otto responds by using backward induction. Using backward induction requires the following steps. Decision-makers start at the end of the game. The player making the last decision chooses the decision that has the greatest payoff. As a result, the player making a decision in the step before the last decision takes into account the likely decision in the last step when making her decision. Decision-makers continue working backward from the last decision, taking into account the likely decision made at each step in the sequence, until the first step — the initial decision step — is reached. Figure 12-4 illustrates the backward induction process.
Figure 12-4: Backward induction.
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