(Based on Roy Gardner, Games for Business and Economics) Two competing firms are deciding how much to invest in advertising. They can choose a low budget (L) or a high budget (H). The payoffs are as follows: L L 100, 100 H 120, 40 H 40, 120 60,60 What is the solution to this game? How does this game resemble the Prisoners' Dilemma?

(Based on Roy Gardner, Games for Business and Economics) Two competing firms are deciding how much to invest in advertising. They can choose a low budget (L) or a high budget (H). The payoffs are as follows: L L 100, 100 H 120, 40 H 40, 120 60,60 What is the solution to this game? How does this game resemble the Prisoners' Dilemma?

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5PA

See similar textbooks

Similar questions

5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
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
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 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)?
5. Aaron and Betty play the following one-shot game. Aaron Up Middle Down Left 10,0 5,10 1,1 Betty Right 0,5 1,0 2,2 a. Does the game above have any (pure strategy) Nash equilibria? Find any equilibria or explain why an equilibrium doesn't exist. b. Suppose instead that Aaron moves first and Betty moves second. Represent this situation with a game tree and find the subgame perfect Nash equilibrium. Are Aaron and Betty better off playing a simultaneous game or a sequential game in which Aaron moves first? Explain. c.
Costco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B
5. To advertise or not to advertise Suppose that two firms, Hatte Latte and Bean Bruuer, are the only sellers of espresso in some hypothetical market. The following payoff matrix gives the profit (in millions of dollars) earned by each company depending on whether or not it chooses to advertise: Hatte Latte Advertise Doesn't Advertise Advertise 10, 10 Bean Bruuer 2,18 Doesn't Advertise 18, 2 11, 11 For example, the lower left cell of the matrix shows that if Bean Bruuer advertises and Hatte Latte does not advertise, Bean Bruuer will make a profit of $18 million, and Hatte Latte will make a profit of $2 million. Assume this is a simultaneous game and that Hatte Latte and Bean Bruuer are both profit-maximizing firms. If Hatte Latte chooses to advertise, it will earn a profit of $ does not advertise. If Hatte Latte chooses not to advertise, it will earn a profit of $ Bruuer does not advertise. million if Bean Bruuer advertises and a profit of $ million if Bean Bruuer advertises and a…
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.
5. To advertise or not to advertise Suppose that Fizzo and Pop Hop are the only two firms that sell orange soda. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Рop Hop Advertise Doesn't Advertise Advertise 10, 10 18, 2 Fizzo Doesn't Advertise 2, 18 11, 11 For example, the upper right cell shows that if Fizzo advertises and Pop Hop doesn't advertise, Fizzo will make a profit of $18 million, and Pop Hop will make a profit of $2 million. Assume this is a simultaneous game and that Fizzo and Pop Hop are both profit-maximizing firms. If Fizzo decides to advertise, it will earn a profit of $ million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Fizzo decides not to advertise, it will earn a profit of S million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Pop Hop advertises, Fizzo makes a higher profit if it chooses If Pop Hop…
3. Consider the following payoff matrix for a complementary investment game: WCG a. Do Not Invest C. Invest b. What is the Nash equilibrium? Do Not Invest What is the maximin solution? 0 Does either firm have a dominant strategy? -100 BB 0 0 Invest 0 20 d. How do your answers change if BB loses 5 if it invests and WCG doesn't invest? 110 10
4. This problem is based on after chapter question 11. If you are not familiar with the rule of baseball game, just use the figure below. a. Find the subgame perfect Nash equilibrium. Note: like many sports games we discussed, the equilibrium is often about mixed-strategies. b. What are the equilibrium payoffs of two players? FIGURE PR9.11 The Suicide Squeeze Game Torre Suicide squeeze Torre 10 LaRussa 0 Pitchout No suicide squeeze 2 ∞0 N LaRussa 8 Suicide squeeze No pitchout Suicide squeeze 9 Pitchout No suicide squeeze 4 6 No suicide squeeze Torre LaRussa No pitchout Suicide squeeze 37 No suicide squeeze 5 55 5
2. Consider the following game. Two criminals are thinking about pulling off a bank robbery. The take from the bank would be $20,000 each, but the job requires two people (one to rob the bank and one to drive the getaway car. Each criminal could instead rob a liquor store. The take from robing a liquor store is only $1000 but can be done with one person acting alone. Write the payoff matrix of this game Player A Bank job Liqour store Player B Bank job Liquor store a. What are the Nash equilibria in this game? b. Explain why there can be multiple equilibria in this game. c. How the game will be played if mixed strategies are allowed? Discuss.