You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is. Given that this is ________ (POSITIVE/NEGATIVE), you (SHOULD/ SHOULD NOT) play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is .(Hint: At what probability does playing the final round yield an expected value of zero?)

You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is. Given that this is ________ (POSITIVE/NEGATIVE), you (SHOULD/ SHOULD NOT) play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is .(Hint: At what probability does playing the final round yield an expected value of zero?)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For $3 bet on hitting a 9, if he or she succeeds, the gambler wins $16 plus return of the $3 bet. What is the expected value of this gambling game? (Present your answer in dollars with 2 decimal places but without $ sign)
The Dean is looking for a tenured professor. Monetary incentives are needed to get someone interested, but how much? The Dean decides to use an auction to do the job. Two professors, equally qualified, applied for the position. The two professors are invited to covertly submit their bids to the Dean. The Dean will give the position to the professor who submits the lower bid (if there is a tie, the job is assigned randomly). The professor who gets the job will be paid his/her own bid. Each professor's reservation value for teaching the course is his/her private information. It is common knowledge that their reservation values are independently and uniformly distributed over [0,100]. So if a professor with a reservation value of 60 wins with a bid of 50, his payoff is 60 - 50 = 10. (a) Find a Bayesian Nash equilibrium of the bidding game. (b) Suppose the two professors' reservation values are 60 and 70, respectively. What are their bids in the Bayesian Nash equilibrium youcomputed in…
You are trying to decide between rescuing a puppy or an older dog. You decide to try to assign some numbers to your preferences so you can compare options. You estimate that your utility for a dog that will chew your furniture is 0.1 and your utility for a dog that can go on hikes with you is 0.8. You expect that a puppy will have an 70% chance of chewing your belongings and a 90% chance of going on hikes. What is your expected utility for getting the puppy?
am. 112.
Three politicians are voting on whether to allow themselves a salary increase of$3,500per a year. If they vote in favor of a raise, then they lose some public support, costing them each$1,500 per year. The salary increase passes if two or more politicians vote in favor of it. What is this game’s Nash equilibrium (or equilibria)? Explain. There is no need to draw a payoff matrix.
Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.
You take a position with a large real estate development company as your first job after graduation. Your first big assignment is to sell an office building – you have been informed the company’s cost into the building (and the bottom line price it is willing to accept) is $400,000. You have identified a likely buyer and you assess that his top price is either $500,000 with a probability of .3, $600,000 with a probability of .5, or $1,000,000 with a probability of .2. You have to commit to a posted price – what price will maximize your profitability?
You are considering two options for your next family vacation. You can visit Disney World or Chicago. Your utility from Disney World is 100 if the weather is clear, and 0 if it rains. Chicago is worth a utility of 70 if the weather is clear and a utility of 40 if the weather is rainy. Also assume that the chance of rain at Disney World is going to be 50% and the chance of rain in Chicago is 40%. As a utility maximizer, should you plan to go to Disney World or Chicago? (Explain using relevant equations)
A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either $39 or $104, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder. The following table lists the four possible combinations of bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder with and without the stated reserve price. Bidder 1 Value Bidder 2 Value Probability Price Without Reserve? Price with $104 Reserve Price? ($) ($) ($) $39 $39 0.25 $39 $104 0.25 $104 $39 0.25 $104 $104 0.25 Without a reserve price, the expected price is…
Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Describe the game and find all Nash equilibria in the following situation: Each of two players chooses a non-negative number. In the choice (a1, a2), the payoff of the first player is equal to a1(a2 - a1), and the payoff of the second player is equal to a2(1 – a1 – a2).
You and your roomate are deciding whether to go to a party or not on Friday. Going to the party is fun and gives a benefit of 4. If you go to the party, there is a 50% chance you will get covid. If you do not attend the party but your roommate does and gets covid, there is 80% chance that you will get covid. The impact of getting covid is -10. If both of you stay home, you will not be exposed to covid and will not have fun, leading to a payoff of 0 for both of you. 3. Construct a game matrix based on the description above and find any (c) Nash equilibria. How would your answer change if one roomate was less social and enjoyed (d) partying less than the other? Change the payoff matrix in a way that is both consistent with one roommate being less social than the other and changes the prediction you found in (a). (Note: if you found multiple possible equilibria in (a), changing the outcome could mean either making one of your prior Nash equilbria the only Nash equilibrium or making an…