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This article is about "Utility" in economics and in game theory.
For utility companies and similar concepts, see public utility.
For utilities in computers, see Computer software

In economics, utility is a measure of the satisfaction gained from the consumption of a "package" of goods and services.

The doctrine of utilitarianism saw the maximisation of utility as a moral criterion for the organisation of society. According to utilitarians, such as Jeremy Bentham (1748-1832) and John Stuart Mill (1806-1876), society should aim to maximise the total utility of individuals, aiming for 'the greatest happiness for the greatest number'.

Cardinal and ordinal utility

Utility was originally viewed as a measurable quantity, so that it would be possible to measure the utility of each individual in society, and add this together to give the total utility of all people in society. Society could then aim to maximise the total, or equivalently the average, utility of all people in society. This conception of utility as a measurable quantity that could be aggregated across individuals is called 'cardinal utility'.

The concept of cardinal utility suffers from the lack of an objective way to measure utility, particularly when comparing the utility gained from consumption of a good between one individual and another.

For this reason, neoclassical economics abandoned utility as a foundation for the analysis of economic behaviour, in favour of an analysis based upon preferences. This led to the development of tools such as indifference curves to explain economic behaviour. In this analysis, an individual is simply observed to prefer one choice to another; there is no attempt to explain why one choice is preferred to another, and hence no need for the concept of utility.

It is nonetheless possible, given a set of preferences which satisfy certain criteria of reasonableness, to find a utility function that will explain these preferences. The utility function would give a higher value for one choice that the individual prefers to another choice. Such utility functions are a useful and widely used tool in modern economics.

A utility function to describe a set of preferences is not unique. If the value of the utility function were to be, for example, doubled, squared, or subject to any other strictly monotonically increasing function, it would still describe the preferences correctly. With this approach to utility, known as ordinal utility it is therefore not possible to compare utility between individuals, or find the total utility for society as the Utilitarians hoped to do.

Utility in game theory

In game theory utility is represented as a function representing the anticipated payoff[?] of each player corresponding to their selected strategy. The domain of any utility function is defined below.

Consider a system ζ of entities u, υ, ω

A player has an anticipation[?] in ζ for any given move and their utility function has a natural operation[?] defined as:

αu + (1 - α)υ
where 0 ≤ α ≤ 1 and the probability of u is α(u)
and the probability of υ is (1 - α)(υ).

The correspondence[?] of utility and preference is denoted by:

u → α = V(u)

u being the utility and V(u) the value attached to it.

The following axioms are required:

1) u > υ implies V(u) > V(υ) and is a complete ordering of ζ

2) u and υ can exist only in three mutually exclusive[?] orderings
u > υ; u < υ; u = υ;
and all ζ are fully transitive of order

3) u > υ implies that u > αu + (1 - α)υ

4) u > υ > ω implies that their exists an α such that
αu + (1 - α)υ > ω
therefore α(ζ) is continuous

5) entities in ζ can be combined algebraically such that
αu + (1 - α)υ = (1 - α)υ + αu
α(βu + (1 - β)υ) + (1 - α)υ = γu + (1 - γ)υ
where γ = α(β)

See also microeconomics, expectation utilities.

References and additional reading:

to be merged:

The concept of utility is a quantitative measure of happiness or satisfaction of humankind towards certain commodities. Applied by economists in such topics as the indifference curve, which measures the combination of a basket of commodities that an individual or a community requests at a given level(s) of satisfaction, there are mainly two kinds of measurement of utility implemented by economists:

1. Cardinal measure - Not only does this type of measurement evaluate the preference of an individual towards a certain commodity, but it also looks at the arbitrary number that is assigned to that commodity. Numbers assigned to different goods or services can be compared. A utility of 100 units towards a cup of coke is twice as desirable as a cup of coffee with a utility level of 50 units.

2. Ordinal measure - Only the ordering of such utility is important. A utility of 100 towards an ice-cream is not twice as desirable as a utility of 50 towards candy.

The basic principle of economics assumed that humankind is rational thus maximizes their utility by all means that they could. For instance, one would request more of one good if enough amount is available and he/she has the ability to support him/her to acquire that amount. The utility maximization concept is closely related to the Pareto Maximization, Edgeworth Box and Contract Curve.

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