micro 2 lotteries

.1 Decision under Uncertainty: Introduction, Lotteries, and Preferences

Overview Assumptions: ◮ Uncertainty: decisions do not entail certain outcomes. ◮ Rationality: how do / how should rational players behave? Concepts: ◮ Lotteries ◮ Preferences ◮ Expected utility & underlying assumptions (‘axioms’) ◮ Attitudes toward risk ◮ Comparing lotteries’ riskiness ◮ Limitations Applications/Examples: ◮ Insurance ◮ Portfolio choice ◮ Exam preparation

Decision under Uncertainty ◮ What if some, rather than being certain, some consumption bundles are randomly available? ◮ The good ‘skiing in the Swiss alps’ for instance is only available under certain temperatures. ◮ More generally, the outcome often depends not only on the chosen action, but also chance, the realization of a state of the world. ◮ State of the world may be the weather, or: damage by accident, success or failure on a test, development of a new product, etc.

Questions Ahead ◮ How can we formally describe preferences over decisions with uncertain outcomes? ◮ What is ‘rational behavior’ (optimization using all available info) under uncertainty? ◮ How can we formalize this in an abstract model? ◮ What are (theoretical) predictions regarding empirically observable behavior (positive)? ◮ What are normative implications of theory regarding economic decisions?

Reducing Compound Lotteries ‘Reducing’ compound lottery g into simple lottery: ◮ Collect all possible final outcomes in A. ◮ For each outcome, calculate the probability with which it materializes, given probabilities in g and all compound lotteries in g. ⇒ Yields simple lottery which is implied by g

Preferences over Lotteries ◮ Lotteries describe well defined choice alternatives. ◮ To model choice under uncertainty, we need a model of preferences over lotteries (paralleling ‘utility maximization’ under certainty). ◮ Like under certainty, we would like a utility function U(g), defined over the set of lotteries G

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