May 27, 2011 this lecture explains what we mean when we say rational when we use game theory to describe social science phenomenon. R is concave if and only if for every ntuple of numbers. You dont have to spend time with the formal development, butyouarewelcometodoso. Decision theory stanford encyclopedia of philosophy. Oskar morgenstern wrote the theory of games and economic behavior, one of the great social science books of the 20th century. Third,illprovidean informal discussionoftheexpectedutility property.
The term expected utility is appropriate because with the vnm form, the utility of a lottery can be thought of as the expected value of the utilities unof the noutcomes. Ideal events are events esuch that savages sure thing principle holds for eand ec. Decision theory is concerned with the reasoning underlying an agents choices, whether this is a mundane choice between taking the bus or getting a taxi, or a more farreaching choice about whether to pursue a demanding political career. Rk isconvexif it contains the line segment connecting any two of its members. Remarkably, they viewed the development of the expected utility model. Under what conditions will he insure, and for how much of the loss. Expected utility theory an overview sciencedirect topics.
Cant have a real utility function on consequences, as consumer never. Invented expected utility, hedging strategies, and a. Econ 4515 finance theory 1 diderik lund, october 2004 write x. Lecture 11 risk aversion, expected utility theory insurance. In this book, they moved on from bernoullis formulation of a utlity function over wealth, and defined an expected utility function over lotteries, or gambles. Uncertainty, expected utility theory and the market. The core idea behind utility theory is that every possible action or state within a given model can be described with a single, uniform value.
Prudence coefficient and precautionary savings dd5 7. To make use of this decision theoretic foundation in portfolio construction, markowitz approximated the vnm expected utility theory by his wellknown mv utility function from levy and markowitz 1979. Another example of a utility function that might be used to examine choice under uncertainty is the cobbdouglas utility function. Examining expected utility theory from descriptive and. Two potential values y1 or y2 probabilities are either p1 or p21p1 when incomes are realized, consumer will experience a particular level of income and hence utility but, looking at the problem beforehand, a person has a particular expected utility. It is a logiclike criterion of consistency and coherence, recommended 4a slightly different categorization is given by suppes 277.
Notes on uncertainty and expected utility ted bergstrom, ucsb economics 210a november 16, 2016 1 introduction expected utility theory has a remarkably long history, predating adam smith by a generation and marginal utility theory by about a century. Basic utility theory for portfolio selection in economics and nance, the most popular approach to the problem of choice under uncertainty is the expected utility eu hypothesis. The purpose of the extension to nonideal acts is to accommodate welldocumented deviations from expected utility theory. One of the central accomplishments is the rigorous proof that comparative preference methods over fairly complicated event spaces are no more expressive than. In words, for someone with vnm expected utility preferences, the utility index of this lottery is simply the expected utility of the lottery, that is the utility of each bundle x 1,x 2 weighted by its prior probability. Prudence coefficient and precautionary savingsprudence coefficient and precautionary savings dd5 6.
Insurance isactuarially fair,subfair, orsuperfairif the expected net payout per unit, p q, is 0, 0, respectively. The deeply nontrivial step in savages contribution is to reveal these two items simultaneously from the axiomatically constrained preference behavior. In the next 3 sections we develop alternative theories for choices under risk. Random utility theory models an agents preferences on alternatives by drawing a realvalued score on each alternative typically independently from a param eterized distribution, and then ranking the alternatives according to scores. The independence axiom says that i prefer pto p0, ill also prefer the possibility. We start with the mainstream theory in economics the expected utility theory eut. Pareto optimality and competitive equilibrium, welfare theorems, the competitive model, bilaterial.
Do you think suicide terrorists are inherently rational. Sharing decision utility is sharing power, not welfare 3. By the substitutability axiom, the consumer will be indi. He failed, however, to fully spell out these implications in any further detail. Prescriptive utility theory in prescriptive utility theory a preference assumption is often viewed as a commonsense guideline for the individual to follow in identifying his preferences explicitly. We show that every welfaremaximizing mechanism entices participation and that the converse holds under additional assumptions. Contextual strength cs of preferences, and vnm preference as strong preference cs henceforth, i explicitly distinguish the terms vnm preference and vnm indifference as those axiomatized by vnm, interpreted as. As a corollary, we obtain a characterization of an attractive randomized voting. F and a,letfagdenote the act that agrees with f on aand with gon the ac, the complement of a. The theory states that rational agents always attempt to maximize their expected utility, defined as the probabilityweighted average of the vnm utility of each final state of wealth. Much of economics builds on expected utility theory, but economists also study alternative hypotheses that may shed light on some phenomena e. Expected uncertain utility theory princeton university. Note that agent here stands for an entity, usually an individual person, that is capable of. Using vnm expected utility theory to facilitate the decision making in social ethics to demonstrate the limits of the application of classical utilitarianism in applied ethics as well as the advantages of introducing quantification techniques, what follows in this paper is a case study.