Expected utility

TABLE 9-12 Comparison of Projects in Terms of Expected Value and Expected Utility... 

Project (NPV), Prohahility, P Equivalent prohahility of winning 100,000 Prohahle utility Expected value, Expected utility, ... 

Evaluate isothermal aging characteristics of thermally unstable components at the maximum expected utility temperature... 

The theory of decision making under risk tells people to maximize expected utility. In cases like the one 1 have just discussed, this means the same as utility averaged over many periods. The theory has been extended, however, to cover choice situations that do not repeal themselves day after day or year after year. In that case the decision maker is asked to rely on his "subjective probabilities" or, in less solemn language, on his informed hunches. The utility of each possible outcome of an action is weighted by the estimated probability of that outcome, to yield the expected utility of the action. The theory tells us to take the action that has associated with it the highest expected utility. In the next chapter 1 state my reasons for being skeptical about this extension of the theory. 

We at once see two equilibria. In each, one player swerves and the other docs not. In addition, there is a third equilibrium, in which each player decides to swerve with probability. Look at the situation from Paul s point of view. He expects Peter to swerve with probability f. What is his best response With what probability p should he decide to swerve His expected utility... 

Preliminary results confirm the expected utility of direct ionic substitution reations for the preparation of derivatives of diamantane. In refluxing bromine, diamantane gives 1-bromodiamantane (74) 26S> as well as a variety of disubstituted bridgehead bromides (Eq. (64)) 266 If, on the other hand, the reaction is carried out in the presence of AlBr3, significant amounts of 4,9-dibromodiamantane, 77, are also observed (Eq. (65) 265l Treatment of this dibromide with one equivalent of trialkyltin hydride yields the 4-mono-substituted diamantane, 78. 

Betting Tversky and Fox1 said that there is a pattern that violates the expected utility theory as follows 112 Stanford students were asked to choose between prospects defined by the outcome of an upcoming football game between Stanford and the University of California at Berkeley. Each participant was presented with three pairs of prospects displayed in Table 6.2. The percentage of respondents who chose each prospect appears on the right-hand side. ... 

Table 6.2 shows that, overall, f, was chosen over g, f2 over g2, and g3 over f3. Furthermore, the triple (I), f2, g3) was the single most common pattern, selected by 36% of the respondents. This pattern violates expected utility theory, which implies that a person who chooses I) over g and f2 over g2 should also choose f3 over g3. However, 64% of the... 

Let Pt and Vt be the probability that the event-/ occurs and the utility function of event-/, respectively. People act as the expected utility that is expressed as... 

The straight line in Fig. 9-25 represents the situation in which the expected value and the expected utility are equal over the range of - 100,000 to... 

In this example, the order of priorities based on expected utilities is the same as that based on expected values. However, the order of priorities is clear-cut on the basis of expected value but much less so on the basis of expected utility. 

The individual s problem is to maximize his expected utility in (1) subject to the budget constraint... 

There are two aspects to any fully Bayesian approach. The first is the mechanics of producing a posterior distribution for the bioavailability ratio. Various approaches have been proposed (Fluehler et al, 1983 Mandallaz and Mau, 1981 Racine et cd., 1986 Selwyn et al, 1981 Selwyn and Hall, 1984). The second aspect is the practical decision rule which should link the posterior distribution to a declaration of equivalence or Inequivalence as the case may be. To be fiiUy Bayesian, the utilities associated with declaring equivalence or inequivalence should be established as a function of the true bioavailability ratio. For a given posterior distribution the declaration with maximum expected utility should be made. 

Thus, the sum across household members of their marginal willingness to pay is set equal to the market price of the health good, in order to arrive at the definition of the value of statistical life, assume a two-states world, and also that the expected utility of individual h can be written as follows ... 

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