lec22 - 15.053 May 16, 2006 Decision Analysis 2 Utility...

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1 15.053 May 16, 2006 Decision Analysis 2 Utility Theory The Value of Information
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2 No sensible decision can be made any longer without taking into account not only the world as it is, but the world as it will be. . . . Isaac Asimov (1920 - 1992) A wise man makes his own decisions, an ignorant man follows public opinion. Chinese Proverb It doesn't matter which side of the fence you get off on sometimes. What matters most is getting off. You cannot make progress without making decisions.” Jim Rohn Quote of the day
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Lotteries and Utility .5 L1 $50,000 Lottery 1: a 50% chance at $50,000 and a 50% $ 0 chance of nothing. L2 .5 Lottery 2: a sure $20,000 bet of $20,000 How many prefer Lottery 1 to Lottery 2? How many prefer Lottery 2 to Lottery 1? In terms of expected values, L1 is worth $25,000 and L2 is worth $20,000. When I ask students which they prefer, usually 19 out of 20 students state that they prefer L2. (I suspect that the remaining student would actually take L2 if given the choice in reality instead of hypothetically.) This reveals that we do not judge lotteries (or uncertain decisions) solely in terms of expected value. The preference of L2 to L1 shows risk aversion. We are willing to sacrifice expected value in order to reduce the uncertainty. If one wants to use decision trees, this immediately brings up a quandary. If we evaluate each event node of a decision tree using the expected value criterion, can a person who is risk averse use a decision tree? The surprising answer is yes, as we shall soon see. 3
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Attitudes towards risk $50,000 Lottery 1: a 50% chance at $50,000 and a $ 0 50% chance of nothing. .5 L1 .5 L2 $ K Lottery L2: a sure bet of $ K Suppose that Lottery 1 is worth a sure bet of $K to you. If K = $25,000, then you are risk neutral . If K < $25,000, then you are risk averse or risk avoiding . If K > $25,000, then you are risk preferring . A person who values lotteries according to their expected values is called “risk neutral.” Many people are risk neutral when the lotteries involve small amounts, but tend to be risk averse with larger amounts. A person who is willing to sacrifice expected value in order to reduce the risk or uncertainty is called “risk averse” or “risk avoiding”. Most people when faced with lotteries such as L1 and L2 will be risk averse if the amounts of money involved are sufficiently large. A person who is willing to sacrifice money in order to increase risk is called “risk preferring.” This is characteristic of someone who prefers uncertainty and risk. Risk aversion and risk preference is actually quite a complex topic, and a person’s attitude towards risk depends a lot on the context for the lotteries. But we shall assume here that a person is risk averse. 4
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Overview of Utility Theory z If a person is risk averse or risk preferring, it is still possible to use decision tree analysis.
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This note was uploaded on 01/17/2012 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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lec22 - 15.053 May 16, 2006 Decision Analysis 2 Utility...

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