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A single-attribute utility function maps the amount of money a person has (or gains), to a number representing the subjective satisfaction he derives from it. The motivation to define a utility function comes from the St. Petersburg paradox: the observation that people are not willing to pay much for a lottery, even if its expected monetary gain is infinite.
The notion of social utility is analogous to the notion of a utility function in consumer choice. However, a social welfare function is different in that it is a mapping of individual utility functions onto a single output, in a way that accounts for the judgments of everyone in a society.
Exponential Utility Function for different risk profiles. In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present, in which case expected utility is maximized. Formally, exponential utility is given by:
Hence, his utility is (,). In a cloud computing environment, there is a large server that runs many different tasks. Suppose a certain type of a task requires 2 CPUs, 3 gigabytes of memory and 4 gigabytes of disk-space to complete. The utility of the user is equal to the number of completed tasks.
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
If the number of possible bundles is finite, u can be constructed directly as explained by von Neumann and Morgenstern (VNM): order the bundles from least preferred to most preferred, assign utility 0 to the former and utility 1 to the latter, and assign to each bundle in between a utility equal to the probability of an equivalent lottery.
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Standard utility functions represent ordinal preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility cardinal (though still not comparable across individuals). Although the expected utility hypothesis is standard in economic modelling, it has been found to be violated in psychological experiments.