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Behavioral Mathematics for Game AI by Dave Mark

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Multiple Utility Thresholds

Up until this point, we have been envisioning utility curves as being somewhat asymptotic. That is, they curve in a single direction, approaching either a specific value or a particular slope. There are times when utility curves—both for risk and reward—may reverse themselves. This has the effect of making the extra value risked “worth it” again.

The quandary posed by the St. Petersburg paradox is a staple of many of the game shows that we see on TV these days. Games like Who Wants to Be a Millionaire and Deal or No Deal have a component to them that encourages the players to weigh the marginal utility of the money they could win by continuing. There is an assumption that, as we saw in Figure 8.9, a person will reach ...

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