5. Consider this "all-pay" auction in which the highest bidder wins and both bidders must pay an amount equal to theirbid regardless of whether they win or lose. It is common knowledge that Bidder 1 has a valuation of 2 and Bidder 2 hasa valuation of 3. The bids must be whole numbers and Bidder 2 wins in the event of tie. Which of the following areNash equilibria?Bidder 212340, 30, 20, 10, 00, -111, 0-1, 2-1, 1-1, O-1, -1Bidder 120, 00, -1-2, 1-2, 0-2, -13-1, 0-1, -1-1, -2-3, 0-3, -14-2,0-2, -1-2, -2-2, -3-4, -1Note: The notation [0], [1], etc. denotes the pure strategies in which the bidder bids 0,1, etc. Mixed strategies arerepresented by weighted averages of the pure strategies, e.g the mixed strategy in which a bidder bids 1 with aprobability of 1/4 and 4 with a probability of 3/4 is written as 1/4 [1] + 3/4 [4].(5/12 [이 + 1/3 [1] + 1/4 [2], 1/2 [이 + 1/2 [1])O ([0], [0])O (2/3 [0] + 1/3 [1], 1/2 [0] + 1/2 [1])O ([0), [3])O ([0], [1])O None of these optionsO ((1), [0])

Nash equilibrium considers the best response strategy of a player, considering the decision that the…

Answered: Consider this "all-pay" auction in…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.10P

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You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.
A4 The Suboptimality of Lower-Than-Cost Reserve Prices: A seller chooses to sell an object by means of a Vickrey auction. If trade occurs, the seller incurs a positive opportunity cost (i.e. c > 0). There are n > 1 bidders participating in the auction. Suppose that the all of the bidders play according to a symmetric and increasing BNE strategy. Show that the seller is always better off by setting the reserve price equal to her cost (i.e. r = c) than by setting the reserve price below her cost (i.e. r < c).
8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…
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 a similar auction problm as before. Two Örms compete for a contract to build a university building. Their construction costs are independent and uniformly drawn from [0; 1]: (a) Suppose the auction is conducted as follows. Price starts at 1 (at this price both bidders would be happy to win the project). The price goes down continuously: at time t 2 [0;1]; the price will be 1 t. At any time t; any bidder can shout ìáoccinaucinihilipiliÖcious.î Once that happens, the price will stop to decline. The bidder who remains silent becomes the winner and he is paid the price at that moment. If both players say it at the same time, the auction ends without a winner. If no player speaks until t = 1 (and the price will be zero by then), the game ends and a winner is selected randomly for a price of 0: Analyze this auction. You donít have to provide rigorous mathematical proofs. How does this auction relate to (a) or (b)? 1 (b) Suppose the auction is conducted as follows.…
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(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).
What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)
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Suppose your firm is in need of cash and plans to auction off a subsidiary to the highest bidder. Which type of auction will maximize your firm’s revenues from the sale if (1) The bidders are risk neutral and have independent private valuations? (2) The bidders are risk neutral and have affiliated value estimates?
** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…

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