Nick, Mike, Oscar, and Pete have joined together to purchase a partial season ticket package for the Washington Capitals. Because there are twelve home games, each person will get tickets to three games. Each person has ranked the games they prefer from 1 to 12, with 1 being the most preferred and 12 being the least preferred. The table below details these preferences. Person Game Nick Mike Oscar Pete 1- Red Wings 2- Penguins 3 - Rangers 4 - Avalanche 5 - Coyotes 6- Bruins 7- Canadiens 8- Kraken 9- Jets 10 - Islanders 11 - Blues 1. 12 1. 4 4 11 1. 12 8 10 10 7 12 10 12 7 7 11 3 11 11 10 6 2 2 7 12 - Sharks 4 1. 4 2. You are asked to fairly distribute the tickets to each of the four people in such a way that this optimizes their satisfaction and the total satisfaction. Which of the following best describes the constraint for the 5th game (against the Coyotes)? x5N + x5M + x50+ х5P s 2 x5N + x5M + х50+ х5P 2 1 x5N + x5M + x50 + x5P = 2 x5N + x5M + x50 + x5P s 1 x5N + x5M + x50 + x5P 2 2 x5N + x5M + x50 + x5P = 1 None of these answers are correct.

Nick, Mike, Oscar, and Pete have joined together to purchase a partial season ticket package for the Washington Capitals. Because there are twelve home games, each person will get tickets to three games. Each person has ranked the games they prefer from 1 to 12, with 1 being the most preferred and 12 being the least preferred. The table below details these preferences. Person Game Nick Mike Oscar Pete 1- Red Wings 2- Penguins 3 - Rangers 4 - Avalanche 5 - Coyotes 6- Bruins 7- Canadiens 8- Kraken 9- Jets 10 - Islanders 11 - Blues 1. 12 1. 4 4 11 1. 12 8 10 10 7 12 10 12 7 7 11 3 11 11 10 6 2 2 7 12 - Sharks 4 1. 4 2. You are asked to fairly distribute the tickets to each of the four people in such a way that this optimizes their satisfaction and the total satisfaction. Which of the following best describes the constraint for the 5th game (against the Coyotes)? x5N + x5M + x50+ х5P s 2 x5N + x5M + х50+ х5P 2 1 x5N + x5M + x50 + x5P = 2 x5N + x5M + x50 + x5P s 1 x5N + x5M + x50 + x5P 2 2 x5N + x5M + x50 + x5P = 1 None of these answers are correct.

Principles of Economics, 7th Edition (MindTap Course List)

7th Edition

ISBN:9781285165875

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 7PA

See similar textbooks

Similar questions

Imagine that a zealous prosecutor (P) has accused a defendant (D) of committing a crime. Suppose that the trial involves evidence production by bothparties and that by producing evidence, a litigant increases the probabilityof winning the trial. Specifically, suppose that the probability that the defendant wins is given by eD>(eD + eP), where eD is the expenditure on evidenceproduction by the defendant and eP is the expenditure on evidence production by the prosecutor. Assume that eD and eP are greater than or equal to0. The defendant must pay 8 if he is found guilty, whereas he pays 0 if heis found innocent. The prosecutor receives 8 if she wins and 0 if she losesthe case. (a) Represent this game in normal form.(b) Write the first-order condition and derive the best-response function foreach player.(c) Find the Nash equilibrium of this game. What is the probability that thedefendant wins in equilibrium.(d) Is this outcome efficient? Why?
3.17. Consider the social choice function that selects as a winner thecandidate (or candidates) with the most second-place votes.(a) Show that this method violates monotonicity.(b) Show that this method violates the Pareto criterion.(c) Show that this method is anonymous and neutral.
Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.
Consider the following Bayesian game. There are two players 1 and 2. Both players choose whether to play A or B. Two states are possible, L and R. In the former, players play a stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player 2 knows the state, while Player 1 thinks that the state is L with probability q and R with probability 1 ! q. Payo§s in each state respectively satisfy: Player 1 is the row player, and their payo§ is the first to appear in each entry. Player 2 is thecolumn player and their payo§ is the second to appear in each entry. (a) What is the set of possible strategies for the two players in this game? (b) Find all the pure strategy Bayes Nash equilibria for any value of q 2 (0, 1).
2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?
Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…
There is an election with three candidates: Lady Left (LL). Care Central (CC), and Robert Right (RR). The following are the outcomes in various two- and three-way races: CC. 100%. RR, 0% /LL, 0%. CC/ 100% RR, 51%, LL, 49% RR, 35%. LU 33% CC 329 The voting system is such that first there is a three way race. Then, if none of the three candidates wins more than 50% of the votes, there is a two-way runoff election between the two can Is this voting system consistent? Explain which property of consistency is violated, if any. Short answer
We’ll now show how a college degree can get you a better job even if itdoesn’t make you a better worker. Consider a two-player game between aprospective employee, whom we’ll refer to as the applicant, and an employer. The applicant’s type is her intellect, which may be low, moderate,or high, with probability 1/3 , 1/2 , and 1/6 , respectively. After the applicantlearns her type, she decides whether or not to go to college. The personalcost in gaining a college degree is higher when the applicant is less intelligent, because a less smart student has to work harder if she is to graduate. Assume that the cost of gaining a college degree is 2, 4, and 6 for an applicant who is of high, moderate, and low intelligence, respectively.The employer decides whether to offer the applicant a job as a manageror as a clerk. The applicant’s payoff to being hired as a manager is 15,while the payoff to being a clerk is 10. These payoffs are independent ofthe applicant’s type. The employer’s payoff from…
Two staff managers in the ΠBΦ sorority, the house manager (player 1) and kitchen manager (player 2), must select a resident assistant from a poolof three candidates: {a, b, c}. Player 1 prefers a to b, and b to c. Player 2 prefers b to a, and a toc. The process that is imposed on them is as follows: First, the house manager vetoes one of thecandidates and announces the veto to the central office for staff selection and to the kitchenmanager. Next the kitchen manager vetoes one of the remaining two candidates and announcesit to the central office. Finally the director of the central office assigns the remaining candidateto be a resident assistant at ΠBΦ.a. Model this as an extensive-form game (using a game tree). You will need to define theutilities of both players.b. Find the subgame-perfect Nash equilibrium (or equilibria) for this game. Is it unique?c. Now assume that before the two players play the game, player 2 can send an alienatinge-mail to one of the candidates, which would…
Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
For the students of the college, the visual appearance of the campus is _______(rival/nonrival) and ______(nonexcludable/excludable). Thus, the visual appearance would be classified as a public good. Suppose the college administrators estimate that the beautification initiative will cost $34,980. To decide whether the initiative should be undertaken, administrators conduct a survey of the college's 1,460 students, asking each of them their willingness to pay for the beautification project. The average willingness to pay, as revealed by the survey, is $32. The benefit of the beautification initiative, as suggested by the survey, is $_______. Because the estimated benefit is _______(less/greater) than the cost, the college administrators _______(should not/should) undertake the beautification initiative. The calculation of the benefit of the beautification initiative relied on the ability of the administrators to capture the true willingness to pay of each student accurately. Which…
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?