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Unformatted text preview: Kata Bognar email@example.com Economics 142 Probabilistic Microeconomics UCLA Fall 2009 1 Decision Theory, Lotteries and Expected Utility Readings. Chapter 1-2. The Notes on the Theory of Choice by David M. Kreps is an excellent but challenging book on the topic. The paper Choice Under Uncertainty: Problems Solved and Unsolved by Mark Machina in the Journal of Economic Perspectives (Summer 1987, 1) is a very good survey on the topic. Concepts. Preference relation, transitivity and completeness axioms, utility function. Lotteries, independence axiom, continuity axiom, expected utility. Ordinal and cardinal utility. First order stochastic dominance. 1.1 An Example, Possible Decision Criteria We start with an example to illustrate what sort of decision situations are we talking about here. Imagine that you can pick between the following two uncertain options: the lottery A pays 1 A = $100 with probability 1 / 10 $50 with probability 8 / 10 $0 with probability 1 / 10 while the lottery B pays: B = $90 with probability 8 / 10 $50 with probability 1 / 10 $10 with probability 1 / 10 . From now on, we call such uncertain prospect a lottery ; if the possible prizes are different dollar amounts we refer to them as payoffs . Which one would you choose? A pessimist would consider the worst case scenario only, and would probably pick the lottery with the better worst option. In our example, a decision maker who only cares about the worst possibilities would pick B . (Be sure you understand why.) Is this a good way to think about peoples choice? Maybe good for some and not so good for others. However, no individuals who use this so-called maximin criteria would invest. (Make sure you understand why.) We observe that people do invest, so we need something else to explain that. An optimist would consider the wealth in the best scenario, and would probably pick the lottery with the better best option. In our example, a decision maker who only cares about the best scenario would pick A . (Why?) 1 There is a convenient way to represent these lotteries as a tree as we saw it in class. 1 Is this a good way to think about peoples choice? Maybe good for some and not so good for others. However, no individuals who use maximax criteria would buy insurance. (Why?) We observe that people do buy insurance, so we need something else to explain that behavior. Both criteria above considered only the payoffs and ignored the probabilities with which those payoffs happen. It is reasonable to think that the probabilities do matter. Choosing A results in a high prize: $100 with a low probability while B gives a somewhat lower prize: $90 but that is quite likely....
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This note was uploaded on 01/25/2010 for the course ECON ECON 142 taught by Professor Bognar during the Fall '09 term at UCLA.
- Fall '09