Consider a Cournot duopoly model, where two firms compete by providing identical goods. The demand for the good is given by P(q; q2) = 20 – 2q1 – 2q2. The marginal cost of firm 1 is a constant $2 per unit. The marginal cost of firm 2 is private information. Firm 1 believes firm 2's marginal cost is $2 with probability 1/2 and $4 with probability 1/2. Find the Bayes' Nash equilibrium of the game. What is the quantity supplied by firm 1? Numerical answer

Consider a Cournot duopoly model, where two firms compete by providing identical goods. The demand for the good is given by P(q; q2) = 20 – 2q1 – 2q2. The marginal cost of firm 1 is a constant $2 per unit. The marginal cost of firm 2 is private information. Firm 1 believes firm 2's marginal cost is $2 with probability 1/2 and $4 with probability 1/2. Find the Bayes' Nash equilibrium of the game. What is the quantity supplied by firm 1? Numerical answer

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter15: Oligopoly And Strategic Behavior

Section: Chapter Questions

Problem 15P

See similar textbooks

Similar questions

Several firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?
Boeing and Airbus have to decide whether to invest in the development of a Super Jumbo for long distance travel; if they both develop successfully the new plane, their profits will drop by 50 millions a year; if only one develop the Super Jumbo, it will make 80 millions a year in additional profits, whereas the profits of the other firm will drop by 30 millions a year; if no firm develops the plane, nothing changes. Based on giveninformation, construct Matrix Representation of Boeing and Airbus Companies game
Olivia is thinking about opening a new bakery (the entrant). There is already a bakery open in her neighborhood (the incumbent), and the owner of the incumbent bakery makes it clear that if Olivia enters the market, they will cut their prices in an attempt to drive the new bakery out of business. Based on the payoff matrix below, is the incumbent’s threat credible? That is, if Olivia opens a new bakery, will the incumbent actually lower their prices? Note: the entrant chooses the row, the incumbent chooses the column High price Low price Enter 1, 2 -1, 1 Don’t enter 0, 10 0, 1 a. Yes, the threat is credible b. No, the threat is not credible
Megan and Martha own competing hair salons that are in the same neighborhood. They are both considering offering their clients discounts in order to increase business. The payoff matrix shows their yearly incomes in thousands of dollars if they offer and do not offer discounts to their customers. If Megan offers a discount, Martha should ________. If Megan offers no discount, Martha should ________. A-not discount; discount. B-not discount; not discount. C-discount; not discount D-discount; discount. E-indeterminate
Burger Doodle, the incumbent firm, wishes to set a limit price of $8 (rather than the profit-maximizing price of $12) to prevent Designer Burger from entering its profitable market. The game tree above shows the payoffs for various decisions. Burger Doodle makes its pricing decision, then Designer Burger decides whether to enter or stay out of the market. If Designer Burger chooses to enter the market, then Burger Doodle may or may not decide to accommodate Designer’s entry by changing its initial price to the Nash equilibrium price of $10. If Burger Doodle canNOT make a credible commitment to maintain its initial price should Designer Burger decide to enter the market, then Burger Doodle will set price equal to $________ at decision node 1 and the outcome _____________(is, is not) a Nash equilibrium.
Which of the following is FALSE for the grim trigger strategy and the infinite horizon repeated Prisoner's Dilemma game illustrated above? A. In the grim trigger strategy profile, if a player chooses D in a period, then both players chooses D forever after that period B. The threshold discount factor for sustaining cooperation under grim trigger strategy depends on the utility numbers in the stage game C. If all utility numbers remain the same but 3 is replaced by 5 in the stage game, then cooperation CANNOT be sustained in this game for all possible values of the discount factor.
Suppose Telkomsel and Indosat are the only two firms in the internet market. They face the following payoff when the want to invest in the research budget: When both companies invest in small budget, Telkomsel will gain Rp 40 billion and Indosat will gain Rp 50 billion. When both of them invest in large budget, Telkomsel will gain Rp 20 billion and Indosat will gain Rp 30 billion. When Telkomsel invest in large budget and Indosat in small budget, Telkomsel will gain Rp 30 billion and Indosat will gain zero. When Telkomsel invest in small budget and Indosat in large budget, Telkomsel will gain zero and Indosat will gain Rp 70 billion. a). Draw the payoff matrix b). Is there a Nash Equilibrium for that case? Explain.
Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget: Synergy's Decision Large Budget Small Budget Dynaco's Decision Large Budget $20 million, $25 million $15 million, $0 Small Budget $0, $60 million $25 million, $30 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy a dominant strategy. If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco a dominant strategy. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.) True False
In the Tech industry, Tesla and Toyota are two famous brands and compete. Recently, both firms are competing to raise funds from the likes of Soft banks and Yes Bank. Tesla is in talks to raise $600 million and speed up its acquisition plans while Toyota plans to secure at least $200 million in a new funding round this year. Since both firms are going the same investors, if both approach the Soft banks then Toyota is guaranteed to raise $200 million while Tesla will receive $400 million. If both approach Yes Bank, then Toyota will definitely receive $600 million while Tesla will get $400 million. However, if Toyota approaches Yes Bank while Tesla pursues Soft bank, they are guaranteed investments worth $400 million and $800 million. On the other hand, if Toyota pursues Soft Bank while Tesla is interested in securing Yes bank’s funding, they each secure $600 million. a) Solve the Nash equilibrium for the above scenario as a simultaneous game. b) Now model the above scenario as a…
In the Cournot duopoly model, each firm assumes that (select all that applies) a. Group of answer choices b. the price of its rival is fixed. c. the output of its rival is fixed. d. rivals will match price cuts but will not match price increases. e. rivals will match all reasonable price changes.
Suppose that two companies – AlphaTech and BetaLabs – are competing for market share and must simultaneously decide whether to develop a new product. Both companies are reluctant to make a decision as it is only economical for one company to develop a new product. Each company earns nothing if they decide not to develop a new product. One company can earn $50 million by developing a new product only if their competitor does not. If both companies decide to develop a new product, they each lose $10 million. Complete the payoff matrix to represent this game. Based on your solution in part (a), determine the maximin solution.
Two players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Select one: a. A trigger strategy will never support (A,A) as an equilibrium b. A tit-for-tat strategy will never support (A,A) as an equilibrium c. A tit-for-tat strategy will support (A,A) as an equilibrium if δ > 0.7 d. A trigger strategy will support (A,A) as an equilibrium if δ > 0.7