MC Qu. 07-42 (Algo) Suppose Firm A and Firm...Suppose Firm A and Firm B are considering whether to invest in a new production technology. For each firm, the payoff to investing (given in thousands of dollars per day) depends uponwhether the other firm invests, as shown in the accompanying payoff matrix.Firm ADon't InvestInvestMultiple ChoiceOWhat is the Nash equilibrium of this game?OInvest9 for A6 for B7 for A3 for BFirm BFirm A invests, and Firm B doesn't invest.Firm A invests, and Firm B invests.Not Invest5 for A7 for BFirm A doesn't invest, and Firm B invests.12 for A8 for BFirm A doesn't invest, and Firm B doesn't invest.

Firm BInvestNot InvestFirm AInvest 9, 6 5, 7 Not Invest 7, 3 12, 8

Suppose Firm A and Firm B are considering whether to invest in a new production technology. For each firm, the payoff to investing (given in thousands of dollars per day) depends upon whether the other firm invests, as shown in the accompanying payoff matrix. Firm A Invest Don't Invest O Multiple Choice Invest 9 for A What is the Nash equilibrium of this game? 6 for B 7 for A 3 for B Firm B Firm A invests, and Firm B doesn't invest. Firm A invests, and Firm B invests. Not Invest 5 for A 7 for B Firm A doesn't invest, and Firm B invests. 12 for A 8 for B Firm A doesn't invest, and Firm B doesn't invest.

Suppose Firm A and Firm B are considering whether to invest in a new production technology. For each firm, the payoff to investing (given in thousands of dollars per day) depends upon whether the other firm invests, as shown in the accompanying payoff matrix. Firm A Invest Don't Invest O Multiple Choice Invest 9 for A What is the Nash equilibrium of this game? 6 for B 7 for A 3 for B Firm B Firm A invests, and Firm B doesn't invest. Firm A invests, and Firm B invests. Not Invest 5 for A 7 for B Firm A doesn't invest, and Firm B invests. 12 for A 8 for B Firm A doesn't invest, and Firm B doesn't invest.

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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answer the ff: Suppose that each company cancharge either a high price for tickets or a low price. Ifone company charges $300, it earns low profit if theother company also charges $300 and high profit ifthe other company charges $600. On the other hand,if the company charges $600, it earns very low profit ifthe other company charges $300 and medium profitif the other company also charges $600.a. Draw the decision box for this game.b. What is the Nash equilibrium in this game?Explain.c. Is there an outcome that would be better than theNash equilibrium for both airlines? How could itbe achieved? Who would lose if it were achieved?
on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
H3. Cooperation in a Finite Game We have seen that if we play the Prisoners' dilemma with finite repetition, there will be no cooperation in the subgame-perfect equilibrium. There are other games, however, when cooperation can be enforced for at least some time in a finite repetition as well. Give an example with explanation. (Hint: consider games with more than one Nash equilibria.)
Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
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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)?
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4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.
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. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that