(Bertrand’s duopoly game with discrete prices) Consider the variant of the example of Bertrand’s duopoly game in this section in which each firm is restricted to choose a price that is an integral number of cents. Assume that c is an integral number of cents and that α > c + 1. Is (c, c) a Nash equilibrium of this game?

(Bertrand’s duopoly game with discrete prices) Consider the variant of the example of Bertrand’s duopoly game in this section in which each firm is restricted to choose a price that is an integral number of cents. Assume that c is an integral number of cents and that α > c + 1. Is (c, c) a Nash equilibrium of this game?

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5CQQ

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1. Find pure strategy Nash equilibrium and find the outcome, that will be played in cooperation. Explain clearly.
Assume a simultaneous-move game. Firm B Low Price High Price Firm A Low Price 10,10 100,2 High Price 2,100 90, 90 What is the Nash equilibrium of the game?
3. There are 2 firms that are considering entering a new market. The payoff for each firm that enters is 100/ n where n is the number of firms that enter. The cost of entering is 62. Find all the pure strategy Nash equilibria. Find the mixed strategy equilibrium.
QUESTION 2 Which of the following statements about a Nash equilibrium is not correct? A. For each finite noncoopertiave game there always exists a pure strategy Nash equilibrium. B. A game has at least two players. C. Each player plays a best response to opponents' Nash strategies. D. No player has a profitable unilateral deviation.
(Table: Samsung and Apple’s Payoff Table) Suppose that a market is dominated by two large firms, Samsung and Apple. Both have two choices: to Advertise or Do not advertise. The payoff table below shows the potential revenues associated with each firm’s strategies. For example, if Apple advertises and Samsung does not, the payoff to Apple is $75,000 and Samsung’s payoff is -$25,000. What are Apple and Samsung’s respective dominant strategies? Apple (right payoffs) Samsung Do not advertise Advertise Do not advertise (50000, 50000) (-25000, 75000) Advertise (75000, -25,000) (10000,10000) Group of answer choices Do not advertise, Do not advertise Advertise, Advertise Do not Advertise, Advertise Advertise, Do not Advertise
Question 1 Assume the market for a product can be described as a Cournot duopoly with two identical firms. The Nash-equilibrium in this market is that the two firms produce the same quantity. Hence, they will have identical market shares, each will have 50%. Assume that firm 1 decides to invest in a technology that reduces its marginal costs. a) What will happen to the two firms market shares? You must explain how you find the answer. b) What will happen to total production and the price of the product? Again, explain your answer.
q19 If you advertise and your rival advertises, you each will earn $4 million in profits. If neither of you advertises, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $1 million and the non-advertising firm will earn $5 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is a. for each firm to not advertise in any year. b. for neither firm to advertise in early years but to advertise in later years. c. for each firm to advertise every year. d. for each firm to advertise in early years but not advertise in later years.
2. Consider the following game. Assume that this game is played simultaneously and without collusion. The two companies are choosing between two strategies: go international or stay national. The outcomes of each strategy for each company are given the following payoff matrix: a) Find Nash equilibrium in this game. Interpret the equilibrium you found. b) What is the Chipco's dominant strategy, if it has one? How shall Chipco's payoffs change for it to not have a dominant strategy anymore?
1. Suppose Company A is about to play a game with Company B. The following facts are known about the two players. The first Company (Company A) is a row player and uses three different strategies i.e. (Strategy X, Strategy Y and Strategy Z). Whereas the column player (Company B) has two different strategies i.e. (M and N) that can be used accordingly. The payoff matrix is given in the table below. Player B Player A M N X -5 3 Y 3 -7 Z -6 5 Answer the following questions based on the information given above a. Determine the strategies of each firm using graphical technique b. Compute the value of the game.
Game theory Nash equilibrium 1. A slight increase in the marginal cost of a firm definitely leads to a reduction in its output if the firm competes in the: A. Sweezy fashion. B. Cournot fashion. C. Bertrand fashion. D. Cournot fashion and Bertrand fashion. Please explain your answer 2. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.
Refer to the normal-form game of price competition in the payoff matrix below. Suppose the game is infinitely repeated, and the interest rate is 10 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. (a) If both firms stick to this agreement, then what is the present value of firm A's payoffs? Please show your calculations. (b) If firm A cheats, what is the present value of the returns for Firm A for cheating? Please show your calculations.
q52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.