4. Firm 1 and firm 2 are car producers. Each has the option of producing either a big car or a small car. The payoffs to each of the four possible combinations are given in the following payoff matrix. Each firm must make its choice without knowing what the other has chosen. The first number in each cell refers to the payoffs for Firm 2. FIRM 2 Big Car Small Car COMPANY ABC FIRM 1 Low Price Big Car 400, 400 High Price 800, 1000 a. Does either firm have a dominant strategy in this case? Explain your answer clearly. b. Identify all Nash equilibria for this game. Suppose there are 2 players in a non-cooperative game theory situation. Company ABC and Company JKL both sell books and can choose to charge a high price or a low price for a particular book that is very popular. The following matrix contains the payoffs that each company receives under 4 scenarios. The first number in each cell refers to the payoffs for Company ABC. COMPANY JKL Small Car Low Price 1000, 800 200, 300 100, 600 500, 500 High Price 500, 200 150, 100 c. Draw the extensive form of this game. d. If ABC were able to move first in a sequential version of this game, what would the equilibrium be? 4. Firm 1 and firm 2 are car producers. Each has the option of producing either a big car or asmall car. The payoffs to each of the four possible combinations are given in the followingpayoff matrix. Each firm must make its choice without knowing what the other has chosen.The first number in each cell refers to the payoffs for Firm 2.FIRM 2Big CarSmall CarCOMPANY ABCFIRM 1Low PriceBig Car400, 400800, 1000a. Does either firm have a dominant strategy in this case? Explain your answer clearly.b. Identify all Nash equilibria for this game.High PriceSuppose there are 2 players in a non-cooperative game theory situation. Company ABC andCompany JKL both sell books and can choose to charge a high price or a low price for aparticular book that is very popular. The following matrix contains the payoffs that eachcompany receives under 4 scenarios. The first number in each cell refers to the payoffs forCompany ABC.Small CarCOMPANY JKL1000, 800500, 500Low Price200, 300100, 600High Price500, 200150, 100c. Draw the extensive form of this game.d. If ABC were able to move first in a sequential version of this game, what would theequilibrium be?

Nash equilibrium is a concept in game theory that describes a situation in which each participant or…

Answered: 4. Firm 1 and firm 2 are car producers.…

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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4. Firm 1 and firm 2 are car producers. Each has the option of producing either a big car or a small car. The payoffs to each of the four possible combinations are given in the following payoff matrix. Each firm must make its choice without knowing what the other has chosen. The first number in each cell refers to the payoffs for Firm 2. FIRM 2 Big Car Small Car COMPANY ABC FIRM 1 Low Price Big Car 400, 400 High Price 800, 1000 a. Does either firm have a dominant strategy in this case? Explain your answer clearly. b. Identify all Nash equilibria for this game. Suppose there are 2 players in a non-cooperative game theory situation. Company ABC and Company JKL both sell books and can choose to charge a high price or a low price for a particular book that is very popular. The following matrix contains the payoffs that each company receives under 4 scenarios. The first number in each cell refers to the payoffs for Company ABC. COMPANY JKL Small Car Low Price 1000, 800 200, 300 100, 600 500, 500 High Price 500, 200 150, 100 c. Draw the extensive form of this game. d. If ABC were able to move first in a sequential version of this game, what would the equilibrium be?

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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