Rational in the sense defined by the expected utility theory

Reference no: EM13818761

Problem 1 Suppose you have asked your friend Peter if he prefers a sure payment of $20 or a lottery in which he gets $15 with probability 0.5 and $10 with probability 0.5. Is it rational for Peter to prefer the sure payment over the lottery? Is it rational to prefer the lottery over the sure payment? Is it rational to be indifferent between the lottery and the sure payment? Would your answer be any different had I asked you the same question but with A substituted for $20, B for $15 and C for $10? What is the general lesson to learn from this exercise?

Problem 2 George tells you that he prefers more money over less. George also tells you about his preference between a lottery in which he gets $30 with probability 0.9 and 0 with probability 0.1 and a sure payment of $20. Assume that George is rational. Is it possible for him to prefer the lottery over the sure payment? Is it possible to prefer the sure payment over the lottery? Is it possible for him to be indifferent between the sure payment and the lottery? What is the general lesson to learn from this exercise?

Problem 3

Paul told you that he is indifferent between a lottery in which he gets A with probability 0.8 and C with probability 0.2 and a lottery in which he gets A with probability 0.5 and B with probability 0.5. Paul told you also that he prefers a lottery in which he gets A with probability 0.3 and C with probability 0.7 over a lottery in which he gets B with probability 0.5 and C with probability 0.5. Is Paul's preference relation rational?

Problem 4

Tom prefers A over B and B over C. Also, Tom is indifferent between a lottery in which he gets C with probability p and A with probability 1-p and a lottery in which he gets B with probability p and C with probability 1-p. The value of p in both lotteries is the same. For what values of p would Tom's preferences be rational in the sense of von Neumann- Morgenstern's expected utility theory?

Problem 5:

An old lady is looking for help crossing the street. Only one person is needed to help her; more are okay but no better than one. You and I are the two people in the vicinity who can help; we have to choose simultaneously whether to do so. Each of us will gain (get pleasure) 3 "utiles" from her success, no matter who helps her. But each one who goes to help will bear a cost of 1 utile, this being the utility of our time taken up in helping. With no cost incurred and no pleasure derived our payoff is 0. Set this up as a normal form game.

Can you solve the game through iterated dominance?

Problem 7:

Using only 0 and 1 as payoffs construct a 4 x 4 game which can be solved through iterated dominance in the maximal possible number of steps.

Problem 8:

(after Kreps 1988) Assume that the President has the following preferences over any two strategies S and S* on how to conduct a war: When choosing between S and S* prefer S if and only if (1) it gives a lower probability of losing or (2) in case they both give the same probability of losing, when S gives a higher probability of winning. Suppose that we have three possible outcomes of a war: win, lose and draw. A strategy is understood as a probability distribution on the three possible outcomes.

(i) Is this preference relation rational in the sense defined by the preference theory?

(ii) (ii) Is this preference relation rational in the sense defined by the expected utility theory?

Reference no: EM13818761

Questions Cloud

List the current members on the board of governors : Go to the Federal Reserve website: or any other related website, and find the following information: List the current members on the Board of Governors of the Federal Reserve System.

Create an application that allows the user to enter the data : Create an application that allows the user to enter the following employee data

Identifying areas about market research : Reviewing the information in this week's readings and sources you identify in your own research. Identifying areas about market research that are particularly interesting to you or that you would like to know more about

Determining the gross pay for the week : Sue works 46 hours at her job during the week. She is paid $13.30/hour and receives overtime at the rate of time-and-one-half for hours worked over forty.

Rational in the sense defined by the expected utility theory : Is this preference relation rational in the sense defined by the preference theory - Is this preference relation rational in the sense defined by the expected utility theory?

Compare success of individual incentive and group incentive : Compare and contrast the likely success of individual incentives, group incentives, and company wide incentives for improving employee performance.

Moving average forecasting : Moving average forecasting models are powerful tools that help managers in making educated forecasting decisions. A moving average is mainly used to forecast short historical range data. This tool along with other forecasting tools is now computer..

Assignment on hd-dvd versus blu-ray : HD-DVD versus Blu-ray

What are the advantages and disadvantages of cloud computing : What are the advantages and disadvantages of cloud computing. What can the technology bring to your organization

User Account

All Pages