probability b.5. 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 anThe College Signaling GameApplicantCollegeEmployerManagerApplicant 9Employer 4ClerkManager47154LowNocollegeManagerClerkCollege107116Nature67ModerateClerkManager156NocollegeHigh107CollegeManagerClerk1314ClerkManager871514NocollegeClerk107

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5. We'll now show how a college degree can get you a better job even if it doesn't make you a better worker. Consider a two-player game between a prospective employee, whom we'll refer to as the applicant, and an The College Signaling Game Nature

5. We'll now show how a college degree can get you a better job even if it doesn't make you a better worker. Consider a two-player game between a prospective employee, whom we'll refer to as the applicant, and an The College Signaling Game Nature

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 18.1IP

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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…
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.
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…
Professor can give a TA scholarship for a maximum of 2 years. At the beginning of each year professor Hahn decides whether he will give a scholarship to Gong Yi or not. Gong Yi can get a scholarship in t=2, only if he gets it in t=1. Basically, the professor and TA will play the following game twice. TA can be a Hardworking type with probably 0.3 and can be a Lazy type with a probability of 0.7. Professor does not know TA's type. If TA is hard working, it will be X=5 and TA will always work if he gets a scholarship. If TA is lazy, it will be X= 1. There is no time discount for t=2. Find out a Perfect Bayesian Equilibrium of the game.
You like your job, but your boss gives lousy bonuses. You were recently offered a new job with better rewards and your friend wants to know if you intend to take it. You say, "It depends on whether the bonus this year is generous, Let's wait and see. We'll find out next week" The likely outcome of this game is your boss gives you a ousy :bonus and you ept the new job. If you want to stay at your current job and be better rewarded, you could improve your strategy if you: demand an increase in your bonus by a certain amount, but does not tel your boss about the job offer. adopt a dominant strategy to accept the other position and make this known to your boss. O tell the boss about the job offer you are prepared to take if your bonus structure does not increase by a certain amount. Cadopt a dominant strategy to stay at your current position and make this known to your boss.
Consider the game below with a worker (W) and a firm (F). The worker initially can choose to acquire skills or not acquire skills. If the worker does acquire skills, the firm then gets to decide whether to compensate the worker or not. The extensive form of the game and the payoffs are below. Which of the following is true? W Acquirre Not Acquire There is no Nash equilibrium. C Compensate Not Compensate This game has a single Nash equilibrium. There are two Nash equilibria. None of the above. (0,0) Both players have a strictly dominant strategy. (10,10) (-5,20)
In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?
Consider a Variant oF the ultimatum qame We Studicd inclass in which players have Fairness considerations . The timing OF the qame is vSual. First , Player 1 propasar the split (100 -x", x) OF a hundred dellars to player 2,Where XE [0,100]. Player 2 observes split & decides whether to accept (in which case they recieve Money accor ding ti proposed Split) or reject (in Which Case they both get žero dollars).But now player i's Utility equals to her monetary Vtility minus the disutility From unFairneas proportional tO the differene in Monetary OutcCOMeS . That is, qiven a Final Split (m. ,m.) ket u, (m. ,m.) = m, -P. (m, - m2)" %3D U. (m. ,m2) = m,- P2 (m,-m.) Where PP are parametens of the game indicating how strongly Players care a bout Fairness. Note that the case we considered corres pends to B, = B2 = 0 (a) Let B, = To ,P2 = alcept ? revect ? Describe all seguentially rational Strategies For player 2. b) Let B, = 10 ,$=0. For each sequentially rational Strategy of player 2 yoU…
In the signaling game represented below, there are two types of Player 1, smart and dumb, the probabilities of which are 0.4 and 0.6, respectively. Player 1 is in college and can either ((Q)uit or (G)raduate. Player 2 is a prospective employer and can either (N)ot hire or (H)ire Player 1. Player 2's payoff does not depend upon l's education, only her intelligence. Player 1's payoff depends partly on her education: both types benefit from completing their education, but the smart type gets more out of it. Player l's payoff also depends on 2's hiring decision: the smart type wants a job but the weak type does not. 0,0 1, 1 2, 1 0,0 N H N H 2 Q Q .4 C .6 18 G G N H H 2,0 3,1 3, 1 1,0 (a) Find a separating PBE. (b) Find a pooling PBE. (c) , Find an equilibrium in which one type of player 1 mixes, playing both Q and G with positive probability.
b)Rachel’s objective is to maximize the expected profit, subject to that Emma works for Racheland Emma puts effort. However, effort level is not observable. Hence, Rachel needs to writea contract based on the observables. Let’s say, Rachel pays Emma based on the outcome: xLwhen the profit is $0, xM when the profit is $2000, and xH when the profit is $3,000. ThenEmma has three options:(i) Not to work for Rachel(ii) Work for Rachel without effort(iii) Work for Rachel with effortFind Emma’s expected utility on each optionc)ssuming Rachel wants Emma to put effort, her objective essentially becomes to find thelowest contingent payment scheme that is just enough for Emma to work for Rachel, andgives an incentive for Emma to put effort. Formally, we can write this as:min 0.1xL + 0.3xM + 0.6xH ,subject to0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 15, (1)and0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 0.6√xL + 0.3√xM + 0.1√xH . (2)What is Constraint (1) called? What is Constraint (2) called?d) or your information, the…
Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
For questions 32 - 35 consider the following "research and development" game. Firms A and B are contemplating whether or not to invest in R8D. Each has two options: "Invest" and "Abstain." A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn't invent X. it makes 50 in revenue. If a firm invests and is the only one to invent X. it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other's investment decisions. Find the Nash Equilibrium (or Equilibria) of the "research and development" game. There are no Nash Equilibria Invest/Invest Invest/Abstain, and Abstain/Invests…