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TA Handout expected-utility

# TA Handout expected-utility - Expected Utility Suppose an...

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Expected Utility Suppose an agent has \$1 at her disposal, and she is trying to compare the utility of one gamble, say the California state lottery, to that of another gamble, like betting on the UCLA-Stanford football game. How does she decide which gamble is preferable? When agents are comparing di ff erent gambles, or lotteries , under uncertainty, we generally assume that they use the concept of expected utility to evaluate them. A lottery is simply a collection of probabilities describing the odds of a gamble’s outcomes. In our example, if the chance of winning the lottery is 1 in 1,000,000, then L StateLottery = ( π win , π lose ) = ( . 000001 , . 999999). Similarly, if the chance of UCLA beating Stanford is 1 in 4, then L Football = ( π UCLA , π Stanford ) = ( . 25 , . 75). The expected utility of a lottery is simply the weighted average of the utilities, weighted by the probabilities of the outcomes: EU ( L ) = allx π x × u ( x ) In our example, if winning the lottery provides utility of 500,000, and losing yields utility of 0, then the expected utility of L

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