Theory of Expected Utility

Theory of Expected Utility:

St. Petersburg Paradox (Nicholas Bernoulli):

Suppose you had the opportunity to pay $100 and then play of the following gambles, each of which is fair bet.

• You get back $100.

• I toss a fair coin You receive $200 if heads.
Or 0 if tails.

• I roll a fair die You receive
$400 if 1, $70 if 2, $55 if 3, $25 if 4, $40 if 5, and $10 if 6.

All the gambles depicted above have expected value of $100 but would you be equally willing to play each one? For one thing the variances are dissimilar:

• 0

• 1/2 (200 −100)2 + 1/2 (0 −100)2 = 10,000

•1/6(3002+ 302 + 452 + 752 + 602 + 902)= 18,375

You might be more eager to play the gamble with the lower variance than the one with the higher variance.

This point is exemplified by what is called the St. Petersburg paradox. This was illustrious by Bernoulli a Swiss mathematician of the 18th century. He proposed a difference of the following gamble. Suppose a fair coin is tossed until it comes up heads. Your payoff depends on the number of tosses before heads appears for the first time. Recognizing that tosses of a fair coin are independent and that probabilities get multiplied together on successive tosses, your payoffs in Bernoulli’s game are constructed as follows:

$2 if heads comes up first on the first try ( p = 1/ 2 )
$4 if heads comes up first on the second try ( p = 1/ 4 )
$8 if heads comes up first on the third try ( p = 1/ 8 )
$ 2n if heads comes up first on the n-th try (p = 1/ (2)n )

The expected value of the gamble set out above is:

(1/2)2 + (1/4)4 + (1/8)8 + ....(1/2n)2n +.... = ∑ [(1/2n])2n = 1 + 1 + 1 + .... = ∞

However no one would pay an infinite amount to play this gamble. In fact, few would play much more than a few dollars. One reason might be that the discrepancy of this gamble is as well infinite as well as most people prefer lower variance (less uncertainty) to more.

Latest technology based Microeconomics Online Tutoring Assistance

Tutors, at the, take pledge to provide full satisfaction and assurance in Microeconomics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Microeconomics, project ideas and tutorials. We provide email based Microeconomics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Microeconomics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Microeconomics Homework help and assignment help services. They use their experience, as they have solved thousands of the Microeconomics assignments, which may help you to solve your complex issues of Microeconomics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.

©TutorsGlobe All rights reserved 2022-2023.