Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose thatpotential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whicheverstand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below.1/41/23/4Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location?a. One of them puts a stand at 3/4 and the other puts a stand at 1/4b. Chad and Jason put their stands right next to each other at 1/2c. One of them puts a stand at 0 and the other puts a stand at 1d. There is no Nash Equilibrium

If one seller puts a stand at ¾ and other at ¼, the consumers near to them would be attracted to…

Answered: Suppose that Jason and Chad each are…

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 6PA

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Splitting Pizza: You and a friend are in an Italian restaurant, and the owner offers both of you a free eight-slice pizza under the following condition. Each of you must simultaneously announce how many slices you would like; that is, each player i ∈ 1, 2 names his desired amount of pizza, 0 ≤ si ≤ 8. If s1 + s2 ≤ 8 then the players get their demands (and the owner eats any leftover slices). If s1 + s2 > 8, then the players get nothing. Assume that you each care only about how much pizza you individually consume, and the more the better.What outcomes can be supported as pure-strategy Nash equilibria?
3.1 Do either of the two telecommunications firms have a dominant strategy in this interaction?If so, what are these dominant strategies? 3.2 What is the Nash Equilibrium of the game above? Clearly, show the logic you use to reachyour conclusion. What type of game is this? 3.3 Suppose the two firms could incentivize or punish each other, could the two firms find theirway to the socially optimum outcome? How would they do this? After observing the strategic interaction between Globogym and Average Joe’s, the governmentdecides to pass a law that states that the two terms must pre-commit to the quantities of trainingsessions they will supply to the American market.Market demand for training sessions is still modeled as ? = 400 − 0.2?, as before, and the marginalcost of production is constant at R40 per call. Let the number of sessions provided by Globogym berepresented by ?G and the quantity provided by Average Joe’s be represented by ?A. 3.4 Solve the firms’ reaction functions and…
There are a kicker and a goalie who confront each other in a penalty kick that willdetermine the outcome of the game. The kicker can kick the ball left or right, while the goaliecan choose to jump left or right. Because of the speed of the kick, the decisions need to bemade simultaneously. If the goalie jumps in the same direction as the kick, then the goalie winsand the kicker loses. If the goalie jumps in the opposite direction of the kick then the kickerwins and the goalie loses. Model this as a strategic form game and write down the matrix thatrepresents the game you modeled. Find the Nash equilibrium.
You and your friend will divide $4. You have agreed to use the following procedure.Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will chooseyour numbers simultaneously. If the sum of the amounts is less than or equal to $4, theneach of you receives the amount you named and the rest of the money is thrown away.If the sum of the amounts is greater than $4 and the amounts named are different, thenthe person who named the smaller amount receives that amount and the other personreceives the remaining money. If the sum of the amounts is greater than $4 and theamounts named are the same, then each receives $2. (a)Draw the payoff matrix of this game. Let “you” be the row player and “yourfriend” be the column player.(b) Derive the best reply functions of all players.(c) Find the Nash equilibrium (or all of the equilibria) of this game using thebest reply functions you found in part (a).
12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s <w. If an army attacks but its rival does not, no costs are borne by either side. Identify all 12.7 Exercises • 267 the pure-strategy Bayesian Nash equilibria of this game for the following two cases, and briefly describe…
Suppose it is a well-known fact that among ten-year old Ford F-150s, half the trucks are good and half of them are lemons. Suppose that it is also known to all parties that a good truck is worth $8,000 to current owners and $10,000 to potential buyers. A bad truck, on the other hand, is only worth $1,000 to current owners and $2,000 to potential buyers. Throughout, assume that buyers are risk-neutral. 4) Suppose that after much haggling, the current owner is willing to let her truck go for $6,000. What is the most likely implication? a) The truck is a lemon. b) The buyer is an excellent negotiator. c) It's a mutually beneficial transaction.
Jill and Jack both have two pails that can be used to carry water down from a hill. Each makes only one trip down the hill, and each pail of water can be sold for $4. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $2 each to avoid carrying one pail down the hill, and an additional $3 to avoid carrying a second pail down the hill.a. If Jack and Jill each must decide whether to carry one or two pails of water down from the top of the hill, how many pails will each child choose to carry? ___ pail(s)b. Jill and Jack’s parents are worried that the two children don’t cooperate enough with one another. Suppose they make Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, construct the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry. Carry 1 pail Jack Carry 2 pails…
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:…
Suppose an emissions standard is implemented that required each plant to reduce its pollution by 5,000 tons. What will be the Total Cost of Pollution Reduction for the entire industry? Suppose instead of an emissions standard, the government implements a tradeable permit system. Each firm is now given 3,000 permit each (1 permit equals 1 ton of pollution allowed). How many permits will be traded between the 2 firms? (Hint: The total amount that need to be reduced is 10,000 tons. i.e. Q1 + Q2 = 10,000)
It is the week before the Yule Ball Dance, and Victor and Ron are each contemplating whether to ask Hermione. As portrayed above, Victor moves first by deciding whether or not to approach Hermione. (Keep in mind that asking a girl to a dance is more frightening than a rogue bludger). If he gets up the gumption to invite her, then Hermione decides whether or not to accept the invitation and go with Victor. After Victor (and possibly Hermione) have acted, Ron decides whether to conquer his case of nerves (perhaps Harry can trick him by making him think he’s drunk Felix Felicis) and finally tell Hermione how he feels about her (and also invite her to the dance). However, note that his information set is such that he doesn’t know what has happened between Victor and Hermione. Ron doesn’t know whether Victor asked Hermione and, if Victor did, whether Hermione accepted. If Ron does invite Hermione and she is not going with Victor— either because Victor didn’t ask, or he did and she…
Why is information asymmetry not a problem if both parties to an agreementwant the same thing?
We have a group of three friends: Kramer, Jerry and Elaine. Kramer has a $10 banknote that he will auction off, and Jerry and Elaine will be bidding for it. Jerry and Elaine have to submit their bids to Kramer privately, both at the same time. We assume that both Jerry and Elaine only have $2 that day, and the available strategies to each one of them are to bid either$0, $1 or $2. Whoever places the highest bid, wins the $10 banknote. In case of a tie (that is, if Jerry and Elaine submit the same bid), each one of them gets $5. Regardless of who wins the auction, each bidder has to pay to Kramer whatever he or she bid. Does Jerry have any strictly dominant strategy? Does Elaine?

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