4. Consider the following Pricing game. Firms A and B each has two strategies: to charge Low or High price. The following table shows the payoffs for all possible outcomes: Firm B Pricing Strategy Low High Low Firm A 0,0 -200, 400 High 400, -200 100, 100 Suppose that Firms A and B are going to play this game over and over again, forever. Also, suppose both firms agree on the following collusive plan: "We will each charge the high price, provided neither of us has ever charged the low price in any previous period. If one of us cheats and charges the low price, the other player will charge the low price in every period thereafter." Answer the following questions about this infinitely repeated game:

4. Consider the following Pricing game. Firms A and B each has two strategies: to charge Low or High price. The following table shows the payoffs for all possible outcomes: Firm B Pricing Strategy Low High Low Firm A 0,0 -200, 400 High 400, -200 100, 100 Suppose that Firms A and B are going to play this game over and over again, forever. Also, suppose both firms agree on the following collusive plan: "We will each charge the high price, provided neither of us has ever charged the low price in any previous period. If one of us cheats and charges the low price, the other player will charge the low price in every period thereafter." Answer the following questions about this infinitely repeated game:

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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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)?
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.
◄ Search 12:47 PM Sun Nov 12 ← Note Nov 12, 2023 Uptown's price strategy The Nash equilibrium occurs when High Low LED RareAir's price strategy High $12 $15 The more favorable outcome would be for $12 Tt ✪ $6 B Low $6 D $8. $15 $8 S O both firms have an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell A. 92% neither firm has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell D. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell B. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell C. O the firms to collude and use the high-price strategy but this strategy requires cooperation. O one firm to take the lead and let the…
Is this strategy a sub-game perfect Nash Equilibrium? Player 2: a c e Player 1: A DE C 2 True False A d B e a 2 1 2 1 A D E חח 0 0 1 F -1 1000
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
Consider the payoff matrix of Hulu and Netflix. Why don't both firms just raise prices? NETFLIX HULU 15, 15 8, 20 20, 8 10, 10 O It is in each firm's profitable interest to lower prices, no matter what the other competitor does. O Raising prices is illegal in this case. O Firms are concerned about a third competitor entering at higher prices. O Higher prices will increase the number of customers beyond what the firms can handle.
1. Find all subgame perfect nash equilibrium 2. Find a nash equilibrium that is not SPNE, and explain why it is not an SPNE.
15. Consider two competing firms, JR and OG. Suppose OG produces an estab- lished product and JR can either produce a clone or a differentiated product. If JR produces a clone, OG can either sue JR or not sue it. If JR produces a differentiated product rather than a clone, OG can either buy JR or not buy it. The two firms are in a non-cooperative game whose extensive form is rep- resented in the tree diagram below, where the payoffs on the right represent profits. -1 for OG 1 for JR sue OG don't -2 for OG clone sue 1 for JR JR don't clone 1 for OG -1 for JR buy OG don't buy 2 for OG 0 for JR If the two firms' managers are rational and recognize each other as rational, then (a) JR clones and OG sues (b) JR does not clone and OG buys (c) JR does not clone and OG does not buy (d) JR clones and OG does not sue (e) JR clones and OG sues with probability .5
3. In a Stackelberg game, what do we call the firm that moves first? What do we call the firm that moves second?
The following is a payoff matrix for a simultaneous move game between Column and Row: Column Left Middle Right Тор 3, 1 2, 3 10, 2 High 4, 5 3,0 9,4 Row Low 2,2 3,4 12,3 Bottom 5,6 4, 5 9,7 What is the Column's dominant strategy? O Left O Right O Column does not have a dominant strategy O Middle
4. Suppose in 1977 Honda and Toyota each have to decide whether to build an automobile plant in the North American market. The payoff matrix below shows Honda's payoff on the left, and Toyota's on the right. Is there a Nash equilibrium? If so, where, and how do you know? Тoyota Build small Don't build anything plant Build small 16, 16 20, 15 Honda plant Don't build anything 15, 20 18, 18
The next three questions pertain to the following normal-form game played by Pepsi and Coke: Coke Pepsi → | Advertise Don't 3.3 0,5 Advertise 5.0 Don't 4,4 7. Write in the blank Coke's best response to Pepsi, if Pepsi Advertises, 8. If the firms could collude, what pair of actions would they try and agre0 on (write "Advertise" or "Dont" on the line)? Pepsi: Coke: 9. What are the Nash equilibrium strategies of the firms? Coke: Pepsi: