6) Presidënt has a veto power and decisions are made with majority, i.e. at least two votes for the proposal. The board of a company consists of 3 members – the President and two others. The (a) Formulate the situation as a coalition game (write the coalition function) (a) Find the core of the game (b), Find the Shapley value

6) Presidënt has a veto power and decisions are made with majority, i.e. at least two votes for the proposal. The board of a company consists of 3 members – the President and two others. The (a) Formulate the situation as a coalition game (write the coalition function) (a) Find the core of the game (b), Find the Shapley value

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter10: Monopolistic Competition And Oligopoly

Section: Chapter Questions

Problem 13PAE

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(a) Consider a ROCK PAPER SCISSOR game. Two players indicate either Rock, Paper or Scissor simultaneously. The winner is determined by: Rock crushes Scissors, Paper covers Rock, and Scissor cut Paper. In the case of a tie, there is no payoff. In the case of a win, the winner collects 5 dollars. Write the payoff matrix for this game. (b) Find the optimal row and column strategies and the value of the matrix game. 3 2 4 -2 1 -4 5
Question 1 Using your knowledge of the "method of elimination.of dominated strategy". solve for the equilibrium solution(s) to the following pay-off matrix for two players. Player A Player B Strategyl Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy1 (40, 200) Strategy 2 (60, 25) Strategy 3 (88, 55) (55,102) (45, 142) (109) 42) K09. 120) (50, 100) (99, 155)70 la. (80. 100) K104, 55) (44,90) (100,50) C403)165)(17 190 (60, 160) (155,115) (95.120) (50, 90) (84, 100) Strategy 4 Strätegy 5 172) 140) (85, 145) (48, 200) 123)125) (100, 145) Is your solution in "a above unique? Why? b. Present the following extended form of pay-off matrix in a normal form pay-off matrix for the player Extended Form of Pay-»ff Matrix Player B Strategy 1 (40, 20) (30,25) Strategy 2 (90, 300) (85.55) 30 25 Player A Strategy 1 Strategy 2 20
a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?
Boeing and Airbus, change in profits ($m) from the development of a super jumbo jet. airbus airbus develop do not develop boeing develop -50, -50 -30, 80 boeing do not develop 80, -30 0, 0 a) Identify the key assumption of Game theoryb) What important lesson does game theory reveal about coordination inan oligopoly market?c) In the game above, what is the Nash equilibrium?
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38. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their divine services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad and become a Doomer. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. We're all the same bro. (C) You meet at the Orthodox church. (D) There is no focal point. 39. Consider a fractional-reserve banking system in which an initial deposit of $1,000 can generate up to $4,000 in money. What is the reserve ratio? (A) 4 percent. (B) 5 percent. (C) 25 percent. (D) 75 percent.
Up Down Player 1 in the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $100 P2 gets $100 P1 gets $10 P2 gets $10 P1 gets $15 P2 gets $5 P1 gets $110 P2 gets $10
• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)
D Question 11 Consider the following Extended Form Game: O 1 02 O 3 A' 04 (9,5) A P2 P1 B' A' (5,2) (8,5) B x A (1,6) P2 B' According to backwards induction, in how many turn does the game end? P1 B (6,7)
5) The following is a matrix represantation of a simultaneously played game. Alice/Bob Film Ball Game 4,2 0,0 0,0 1,3 a) Draw players' best response functions agains each other Film Ball Game
Two business partners jointly own a firm and share equally the revenues. They individually and simultaneously decide how much effort to put into the firm. Let s₁ and s2 denote the effort choices of partner 1 and partner 2, respectively. Assume si € [0, 4]. The cost of effort is given by s? for i E {1, 2}. The firm's revenue is given by 4(81 +82 + bs182) where 0 ≤ b ≤ 1. (Note that the parameter 6 reflects the synergies between the effort levels. b> 0 implies that the more one partner works, the more productive the other partner is.) The payoffs for partners 1 and 2 are: u₁ (81, 82) u2 (81, 82) - = 1 [4(81 +82 +68182)] − 8² - 1 [4(81 +82 + bs182)] – $²
Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).