Part 1 : Answer the following Games below. For each game below, please illustrate and show how the Nash Equilibrium is derived. Briefly explain the result of each game in not less than 3 sentences. b. You are examining two companies that sell identical products. Company 1 can sell that produce for either Php 17 or Php 27. Meanwhile, Company 2 can sell the produce for either Php 14 or Php 30. The pay-off matrix represents what would be their potential profit for each strategy. What is the Nash Equilibrium? Company 2 Php 14 Php 30 Php 17 3 Compan y1 Php 27 4 7 5 3 4 1 5 LO

Part 1 : Answer the following Games below. For each game below, please illustrate and show how the Nash Equilibrium is derived. Briefly explain the result of each game in not less than 3 sentences. b. You are examining two companies that sell identical products. Company 1 can sell that produce for either Php 17 or Php 27. Meanwhile, Company 2 can sell the produce for either Php 14 or Php 30. The pay-off matrix represents what would be their potential profit for each strategy. What is the Nash Equilibrium? Company 2 Php 14 Php 30 Php 17 3 Compan y1 Php 27 4 7 5 3 4 1 5 LO

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5PA

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20) Given the payoff matrix in the figure, the Nash equilibrium outcome of this game is for: Ajinomoto Produce 30 Produce 40 million pounds million pounds Ajinomoto makes $180 million Ajinomoto makes $200 million Produce 30 million ADM makes $180 million ADM makes $150 million pounds Ajinomoto makes $150 million Ajinomoto makes $160 million Produce 40 million ADM makes $200 million ADM makes $160 million pounds O A. each firm to produce 30 million pounds. B. each firm to produce 40 million pounds. C. ADM to produce 30 million pounds and for Ajinomoto to produce 40 million pounds. D. ADM to produce 40 million pounds and for Ajinomoto to produce 30 million pounds. ADM
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
Please explain it. ASAP
Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
1. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,3
Analyze the following game where Ali is the row player and Ayşe is the column player. U D L R 4, 2 -1, 1 1, -12, 3 1. Find the set of pure strategy Nash equilibria. 2. Draw the game tree of the above-described simultaneous game. 3. Draw the game tree of the above-described simultaneous game as the row player is the first moving player. 4. Find the subgame perfect Nash equilibrium of this game. 5. For those equilibria that are not subgame-perfect, identify the reason (the source of the lack of credibility).
Question 24 In the coordination game shared in class and in the textbook, it shows players Alex and Tyler coordinating over using Microsoft or Apple software. The strategies lead to a situation with two Nash Equilibria where both use Microsoft or both use Apple with each associated with different equal payoffs. This game is illustrating which concept of Network Goods? O The contestability of the market for a network good. O The "best" product may not win. O The coordination amongst competing network goods. O The required scale of success in the market.
4. This problem is based on after chapter question 11. If you are not familiar with the rule of baseball game, just use the figure below. a. Find the subgame perfect Nash equilibrium. Note: like many sports games we discussed, the equilibrium is often about mixed-strategies. b. What are the equilibrium payoffs of two players? FIGURE PR9.11 The Suicide Squeeze Game Torre Suicide squeeze Torre 10 LaRussa 0 Pitchout No suicide squeeze 2 ∞0 N LaRussa 8 Suicide squeeze No pitchout Suicide squeeze 9 Pitchout No suicide squeeze 4 6 No suicide squeeze Torre LaRussa No pitchout Suicide squeeze 37 No suicide squeeze 5 55 5
Q2
Consider the attached game depicted in Normal Form. Find one Nash equilibrium and verify that it is a Nash equilibrium. Note: 1. Remember to express the Nash equilibrium in the form of a strategy profile. 2. Use the definition of Nash equilibrium to verify that the strategy profile you find is really a Nash equilibrium.
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