A partnership will generate revenue p = 2x + y + xy, where x and y are the efforts of partners 1 and 2, respectively. Partners bear effort costs of 2x² and 0.5y2, respectively, and they share the revenue equally. What is the ratio of the equilibrium efforts x/y? 1/2 1
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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?Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?Q56 A Nash equilibrium is an outcome... a. Achieved by cooperation between players in the game. b. That is achieved by collusion where no party has an incentive to change their behaviour. c. Where each player's strategy depends on the behaviour of its opponents. d. That is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player. e. Where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players.
- Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?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)Three players (Allen, Mark, Alice) must divide a cake among them. The cake is divided into three slices.The table below shows the value of each slice in the eyes of each of the players. S1 S2 S3 Allen $7.00 $6.00 $5.00 Mark $4.00 $4.00 $4.00 Alice $5.00 $4.00 $6.00 Which of the slices does Allen deem fair? Group of answer choices S1 and S2 S1 and S3 S2 and S3 S1, S2, and S3 S1 only
- 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…3 7- Consider an election contested by two candidates L & R; when L spends $x million on advertising and R spends $y million. L will get a share x/(x+y) of the votes and R will get y/(x+y). Assume the cost of campaigning is proportional to direct campaign expenditures x & y. Let us suppose that candidate L payoff is measured by its vote percentage minus its advertising expenditure 100 x/(x+y) – x. Similarly, candidate R’s payoff is 100y/(x+y) – y. Find the best response function for each candidate? What is the NE? Is it efficient?A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.
- Melanie and Oli are competing Pacific halibut fishers. Both have been allocated ITQs that limit their catch to 1,000 tons of Pacific halibut each. Melanie's cost per ton is $36; Oli's cost per ton is $40. If the market price of Pacific halibut is $48 per ton, what is the minimum amount per ton that Melanie would have to offer Oli to convince him to sell Melanie his ITQs? Multiple Choice $6. $8. $12. $4.Poker players are known to bluff once in a while, meaning that they will make a large bet despite holding inferior cards in an effort to pressure other players to fold their hands. Would bluffing be considered a dominant strategy in poker? a) No, because if a player bluffs on every hand, other players will catch on and call his or her bluff. b) No, because bluffing is usually not successful and is therefore considered a secondary strategy. c) Yes, because it usually results in a winning hand. d) Yes, because it is the main strategy used by players.Suppose you are one of two producers of aluminium. You (firm 1) and your competitor (firm 2) announce simultaneously the quantities Q1 and Q2 (in tonnes) and earn the profits Q1*P(Q) and Q2*P(Q), respectively, where P(Q) = 50 – Q is the market price per tonne of aluminium and Q = Q1 + Q2 is the total output. Assume, for simplicity, that there are no production costs. a) Can the collusive agreement to produce Q1 = Q2 = 12 tons of aluminium be sustained in a Nash equilibrium of the one-shot game? Explain your answer. b) What is your best response, when firm 2 chooses to produce Q2 = 14 tonnes? Does Q2 = 14 and your best response to it form part of a Nash equilibrium? Explain.…