UrbanPro
true

Search for topics

Expected Utility

Suvam Banerjee
17 Mar 0 0

Expected Utility: Theorems
The theory of expected utility was developed by the founders of game theory, namely John von Neumann and Oskar Morgenstern, in their 1944 book Theory of Games and Economic Behavior.
In a rather unconventional way, we shall first (in this section) state the main result of the theory (which we split into two theorems) and then (in the following section) explain the assumptions (or axioms) behind that result. The reader who is not interested in understanding the conceptual foundations of expected utility theory, but wants to understand what the theory says and how it can be used, can study this section and skip the next. Let O be a set of basic outcomes. Note that a basic outcome need not be a sum of money: it could be the state of an individual’s health, or whether the individual under consideration receives an award, or whether it will rain on the day of her planned outdoor party, etc. Let L (O) be the set of simple lotteries (or probability distributions) over O. We will assume throughout that O is a finite set: O = {o1,o2,..., om} (m ≥ 1). Thus, an element of L (O) is of the form  o1 o2 ... om p1 p2 ... pm  with 0 ≤ pi ≤ 1, for all i = 1,2,...,m, and p1 + p2 +...+ pm = 1. We will use the symbol L (with or without subscript) to denote an element of L (O), that is, a simple lottery. Lotteries are used to represent situations of uncertainty.
For example, if m = 4 and the individual faces the lottery L =  o1 o2 o3 o4 2 5 0 1 5 2 5  , then she knows that, eventually, the outcome will be one and only one of o1,o2,o3,o4, but does not know which one; furthermore, she can quantify her uncertainty by assigning probabilities to these outcomes. We interpret these probabilities either as objectively obtained from relevant (past) data or as subjective estimates by the individual.
For example, an individual who is considering whether or not to insure her bicycle against theft for the following 12 months knows that there are two relevant basic outcomes: either the bicycle will be stolen, or it will not be stolen. Furthermore, she can look up data on past bicycle thefts in her area and use the proportion of stolen bicycles as an “objective” estimate of the probability that her bicycle will be stolen.
Alternatively, she can use a more subjective estimate: she might use a lower probability of theft than suggested by the data because she knows herself to be very conscientious and – unlike other people – always to lock her bicycle when left unattended.
The assignment of zero probability to a particular basic outcome is taken to be an expression of belief, not impossibility: the individual is confident that the outcome will not arise, but she cannot rule out that outcome on logical grounds or by appealing to the laws of nature.

0 Dislike
Follow 2

Please Enter a comment

Submit

Other Lessons for You

Goods and Service Tax
Goods and Services Tax (GST)It is an indirect tax levied by the Central Government. In this tax ·there are so many taxesmerged such as Excise Duty, Customs Duty, Service Tax, Value Added Tax,Entertainment...

Bimal Upadhyay | 19/10/2020

1 0
0

Words Mostly Spelt Wrong
Wrong Correct Cousin brother/sister Cousin Good name name Big blunder blunder Bad dream nightmare No place no room

Shruti K. | 03/09/2020

0 0
0

7 IMPORTANT GRAMMAR RULES
A Noun is a person, place, thing or idea. A vern is an action bird. A complete sentence must include a subject and a predicate. The only exception to the above rules is the imperative sentences. An...

Tiyasha M. | 28/06/2020

0 0
0

All temperatures on the Kelvin scale are in positive figures.
0 K or absolute zero is the lowest temperature on the Kelvin temperature scale and considered as the lowest temperature possible. This is the reason that all temperatures on the Kelvin scale are in positive...

Ajay Mishra | 23/06/2020

0 0
0

Stressed and Unstressed Words in a Sentence
STRESSED AND UNSTRESSED WORDS IN A SENTENCE While speaking, sometimes we give more emphasis to certain words in a sentence or say them louder than others, with extra force. They are called stressed words....

Tanmoy Saha | 01/04/2020

0 0
0
X

Looking for ICSE Schools Classes?

Find best tutors for ICSE Schools Classes by posting a requirement.

  • Post a learning requirement
  • Get customized responses
  • Compare and select the best

Looking for ICSE Schools Classes?

Find best ICSE Schools Classes in your locality on UrbanPro

Post your learning requirement

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more