Chapter 13, Game Theory and Competitive Strategy Video Solutions, Microeconomics

Problem 1

In many oligopolistic industries, the same firms compete over a long period of time, setting prices and observing each other's behavior repeatedly. Given the large number of repetitions, why don't collusive outcomes typically result?

Sanchit Jain

Numerade Educator

02:02

Problem 2

Many industries are often plagued by overcapacity:
Firms simultaneously invest in capacity expansion, so that total capacity far exceeds demand. This happens not only in industries in which demand is highly volatile and unpredictable, but also in industries in which demand is fairly stable. What factors lead to overcapacity? Explain each briefly.

Daniel Cisneros

Numerade Educator

03:21

Problem 3

Two computer firms, $A$ and $B$, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality system (High), or a slower, low-quality system (Low). Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix:
a. If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be?
b. Suppose that both firms try to maximize profits, but that Firm $A$ has a head start in planning and can commit first. Now what will be the outcome? What will be the outcome if Firm $B$ has the head start in
planning and can commit first?
c. Getting a head start costs money. (You have to gear up a large engineering team.) Now consider the two-stage game in which, first, each firm decides how much money to spend to speed up its planning, and, second, it announces which product $(H$ or $L$ ) it will produce. Which firm will spend more to speed up its planning? How much will it spend? Should the other firm spend anything to speed up its planning? Explain.

Foster Wisusik

Numerade Educator

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Problem 4

Two firms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or the low end (low quality). Resulting profits are given by the following payoff matrix:
a. What outcomes, if any, are Nash equilibria?
b. If the managers of both firms are conservative and each follows a maximin strategy, what will be the outcome?
c. What is the cooperative outcome?
d. Which firm benefits most from the cooperative outcome? How much would that firm need to offer the other to persuade it to collude?

Oluwadamilola Ameobi

Numerade Educator

04:26

Problem 5

Two major networks are competing for viewer ratings in the $8: 00-9: 00$ p.m. and $9: 00-10: 00$ p.m. slots on a given weeknight. Each has two shows to fill these time periods and is juggling its lineup. Each can choose to put its "bigger" show first or to place it second in the $9: 00-10: 00$ p.m. slot. The combination of decisions leads to the following "ratings points" results:
a. Find the Nash equilibria for this game, assuming that both networks make their decisions at the same time.
b. If each network is risk-averse and uses a maximin strategy, what will be the resulting equilibrium?
c. What will be the equilibrium if Network 1 makes its selection first? If Network 2 goes first?
d. Suppose the network managers meet to coordinate schedules and Network 1 promises to schedule its big show first. Is this promise credible? What would be the likely outcome?

Michael Jacobsen

Numerade Educator

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Problem 6

Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product $A,$ Product $B,$ or Product $C .$ They will make their choices at the same time. The resulting payoffs are shown below.
a. Are there any Nash equilibria in pure strategies? If so, what are they?
b. If both firms use maximin strategies, what outcome will result?
c. If Firm 1 uses a maximin strategy and Firm 2 knows this, what will Firm 2 do?

Oluwadamilola Ameobi

Numerade Educator

11:04

Problem 7

We can think of U.S. and Japanese trade policies as a prisoners' dilemma. The two countries are considering policies to open or close their import markets. The payoff matrix is shown below.
a. Assume that each country knows the payoff matrix and believes that the other country will act in its own interest. Does either country have a dominant strategy? What will be the equilibrium policies if each country acts rationally to maximize its welfare?
b. Now assume that Japan is not certain that the United States will behave rationally. In particular, Japan is concerned that U.S. politicians may want to penalize Japan even if that does not maximize U.S. welfare. How might this concern affect Japan's choice of strategy? How might this change the equilibrium?

Heather Duong

Numerade Educator

01:29

Problem 8

You are a duopolist producer of a homogeneous good. Both you and your competitor have zero marginal costs. The market demand curve is
\[
P=30-Q
\]
where $Q=Q_{1}+Q_{2} \cdot Q_{1}$ is your output and $Q_{2}$ your competitor's output. Your competitor has also read this book.
a. Suppose you will play this game only once. If you and your competitor must announce your outputs at the same time, how much will you choose to produce? What do you expect your profit to be? Explain.
b. Suppose you are told that you must announce your output before your competitor does. How much will you produce in this case, and how much do you think your competitor will produce? What do you expect your profit to be? Is announcing first an advantage or a disadvantage? Explain briefly. How much would you pay for the option of announcing either first or second?
c. Suppose instead that you are to play the first round of a series of 10 rounds (with the same competitor). In each round, you and your competitor announce your outputs at the same time. You want to maximize the sum of your profits over the 10 rounds. How much will you produce in the first round? How much do you expect to produce in the tenth round? In the ninth round? Explain briefly.
d. Once again you will play a series of 10 rounds. This time, however, in each round your competitor will announce its output before you announce yours. How will your answers to (c) change in this case?

Hunza Gilgit

Numerade Educator

00:38

Problem 9

You play the following bargaining game. Player $A$ moves first and makes Player $B$ an offer for the division of $\$ 100 .$ (For example, Player $A$ could suggest that she take $\$ 60$ and Player $B$ take $\$ 40 .$ ) Player $B$ can accept or reject the offer. If he rejects it, the amount of money available drops to $\$ 90,$ and he then makes an offer for the division of this amount. If Player $A$ rejects this offer, the amount of money drops to $\$ 80$ and Player $A$ makes an offer for its division. If Player $B$ rejects this offer, the amount of money drops to 0 Both players are rational, fully informed, and want to maximize their payoffs. Which player will do best in this game?

Hunza Gilgit

Numerade Educator

13:02

Problem 10

Defendo has decided to introduce a revolutionary video game. As the first firm in the market, it will have a monopoly position for at least some time. In deciding what type of manufacturing plant to build, it has the choice of two technologies. Technology $A$ is publicly available and will result in annual costs of
\[
C^{A}(q)=10+8 q
\]
Technology $B$ is a proprietary technology developed in Defendo's research labs. It involves a higher fixed cost of production but lower marginal costs:
\[
C^{B}(q)=60+2 q
\]
Defendo must decide which technology to adopt. Market demand for the new product is $P=20-Q$ where $Q$ is total industry output.
a. Suppose Defendo were certain that it would maintain its monopoly position in the market for the entire product lifespan (about five years) without threat of entry. Which technology would you advise Defendo to adopt? What would be Defendo's profit given this choice?
b. Suppose Defendo expects its archrival, Offendo, to consider entering the market shortly after Defendo introduces its new product. Offendo will have access only to Technology $A$. If Offendo does enter the market, the two firms will play a Cournot game (in quantities) and arrive at the Cournot-Nash equilibrium.
i. If Defendo adopts Technology $A$ and Offendo enters the market, what will be the profit of each firm? Would Offendo choose to enter the market given these profits?
ii. If Defendo adopts Technology $B$ and Offendo enters the market, what will be the profit of each firm? Would Offendo choose to enter the market given these profits?
iii. Which technology would you advise Defendo to adopt given the threat of possible entry? What will be Defendo's profit given this choice? What will be consumer surplus given this choice?
c. What happens to social welfare (the sum of consumer surplus and producer profit) as a result of the threat of entry in this market? What happens to equilibrium price? What might this imply about the role of potential competition in limiting market power?

Lindsay Bur

Numerade Educator

03:10

Problem 11

Three contestants, $A, B,$ and $C,$ each has a balloon and a pistol. From fixed positions, they fire at each other's balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner gets a $\$ 1000$ prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that $A$ is the best shot and always hits the target, that $B$ hits the target with probability $.9,$ and that $C$ hits the target with probability $.8 .$ Which contestant has the highest probability of winning the $\$ 1000 ?$ Explain why.

Kari Hasz

Numerade Educator

06:18

Problem 12

An antique dealer regularly buys objects at hometown auctions whose bidders are limited to other dealers. Most of her successful bids turn out to be financially worthwhile because she is able to resell the antiques for a profit. On occasion, however, she travels to a nearby town to bid in an auction that is open to the public. She often finds that on the rare occasions in which she does bid successfully, she is disappointed the antique cannot be sold at a profit. Can you explain the difference in her success between the two sets of circumstances?

Tommy Nguyen

Numerade Educator

08:21

Problem 13

You are in the market for a new house and have decided to bid for a house at auction. You believe that the value of the house is between $\$ 125,000$ and $\$ 150,000,$ but you are uncertain as to where in the range it might be. You do know, however, that the seller has reserved the right to withdraw the house from the market if the winning bid is not satisfactory.
a. Should you bid in this auction? Why or why not?
b. Suppose you are a building contractor. You plan to improve the house and then to resell it at a profit. How does this situation affect your answer to (a)? Does it depend on the extent to which your skills are uniquely suitable to improving this particular house?

Rashmi Sinha

Numerade Educator