Deck 10: Game Theory and Competitive Strategy

Question 1

In a bargaining setting with perfect information:

A) backward induction determines the equilibrium outcome.
B) there may be many possible equilibrium outcomes.
C) the equilibrium outcome calls for a 50-50 split of the "pie."
D) the situation represents a constant-sum game.
E) there is a dominant strategy equilibrium.

Answer 1

B

Question 2

Game theory offers insight into:

A) pricing behavior in competitive markets.
B) the optimal output and pricing strategy of a monopolist.
C) the degree of monopoly power enjoyed by a firm.
D) strategic behavior of firms in an oligopoly.
E) adjustment to equilibrium in a monopolistically competitive market.

Answer 2

D

Question 3

Two firms are poised to enter a retail market. Entering the market will be profitable for one firm only if the other firm does not enter the market. This is an example of:

A) prisoner's dilemma.
B) a repeated game with contingent strategies.
C) bargaining game with multiple equilibria
D) a game with a first-mover advantage.
E) a zero-sum game.

Answer 3

D

Question 4

The following table lists the payoffs for Firm 1 and Firm 2 from three possible pricing strategies:
Table 10-3
$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Firm } 2\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { High } & \text { Medium } & \text { Low } \\\hline \text { High } & 3,1 & 4,2 & 2,0 \\\hline \text { Medium } & 2,3 & 5,5 & 3,4 \\\hline \text { Low } & 5,4 & 7,5 & 5,2 \\\hline\end{array}\end{array}$

-Refer to Table 10-3. Identify Firm 2's dominant strategy.

A) Its dominant strategy is medium prices.
B) Firm 2 does not have a dominant strategy.
C) Its dominant strategy is high prices.
D) Its dominant strategy could be high or medium prices depending on Firm 1's response.
E) Its dominant strategy is low prices.

Question 5

A player involved in a one-shot game will:

A) cooperate with its rivals due to the threat of punishment.
B) follow punitive strategies.
C) take actions aimed at creating a reputation with his rivals.
D) act to maximize its immediate payoff.
E) follow a tit-for-tat strategy.

Question 6

Which of the following is true of a sequential game with perfect information?

A) To obtain a complete solution to a sequential game, there should be perfect information.
B) A sequential game with infinite moves can be solved backward to obtain a complete solution.
C) The equilibrium in a sequential game is always a second-best solution.
D) A sequential game does not have a stable equilibrium.
E) The outcome in a sequential game is inferior to the optimal outcome.

Question 7

The following table lists the payoffs for Firm 1 and Firm 2 from three possible pricing strategies:
Table 10-3
$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Firm } 2\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { High } & \text { Medium } & \text { Low } \\\hline \text { High } & 3,1 & 4,2 & 2,0 \\\hline \text { Medium } & 2,3 & 5,5 & 3,4 \\\hline \text { Low } & 5,4 & 7,5 & 5,2 \\\hline\end{array}\end{array}$

-Refer to Table 10-3. Identify Firm 1's dominant strategy.

A) Its dominant strategy is medium prices.
B) Firm 1 does not have a dominant strategy.
C) Its dominant strategy is high prices.
D) Its dominant strategy could be low or medium prices depending on Firm 2's response.
E) Its dominant strategy is low prices.

Question 8

The following payoff table depicts a zero-sum game:
Table 10-4
$\begin{array}{c}\quad\quad\quad\text { Firm 2 }\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { C1 } & \text { C2 } & \text { C3 } \\\hline \text { R1 } & 6 & - 6 & - 4 \\\hline \text { R2 } & - 1 & 3 & - 5 \\\hline \text { R3 } & 3 & 2 & 1 \\\hline\end{array}\end{array}$

-Refer to Table 10-4. The equilibrium of the zero-sum game is:

A) R1 versus C1.
B) R1 versus C2.
C) R2 versus C2.
D) R3 versus C3.
E) R2 versus C3.

Question 9

In an infinitely repeated prisoner's dilemma (such as a repeated price war):

A) repeated defection is the only equilibrium.
B) there are two different equilibria: repeated defection and repeated cooperation.
C) repeated cooperation is the only equilibrium.
D) each player cooperates in the early stages, but defects near the end of the game.
E) there is no stable equilibrium strategy for either player.

Question 10

A game tree diagram is used to represent:

A) a non-zero-sum game.
B) a Nash equilibrium.
C) a simultaneous game.
D) a dominant strategy equilibrium.
E) a sequential game.

Question 11

The key assumption used in game theory is that each player:

A) pursues his own self-interest, taking into account its rival's behavior.
B) is not affected by other players' actions.
C) seeks to outperform its competitors.
D) seeks to maximize the players' collective profits.
E) maximizes its expected utility independent of the rival's actions.

Question 12

The following table lists the payoffs of two firms adopting three possible advertising strategies:
Table 10-5
$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Firm } 2\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { High } & \text { Medium } & \text { Low } \\\hline \text { High } & 3,2 & 4,1 & 5,0 \\\hline \text { Medium } & 1,6 & 5,4 & 3,3 \\\hline \text { Low } & 0,4 & 5,5 & 6,2 \\\hline\end{array}\end{array}$

-Refer to Table 10-5. The (Nash) equilibrium pair of strategies for Firms 1 and 2 is:

A) Low advertising versus high advertising.
B) High advertising for both firms.
C) Medium advertising versus low advertising.
D) High advertising versus low advertising.
E) Medium advertising for both firms.

Question 13

In a competitive situation involving the adoption of a common standard by all firms in the industry:

A) each player should always adopt his own preferred standard to maximize profit.
B) the players will agree upon the standard that maximizes collective profits.
C) the use of dominant strategies will select the appropriate standard.
D) there will be multiple equilibria supporting different possible standards.
E) the players will agree on a compromise between their preferred standards.

Question 14

The following matrix gives the payoffs for Firm 1 and Firm 2 from three possible pricing strategies:
Table 10-1
$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Firm } 2\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { High } & \text { Medium } & \text { Low } \\\hline \text { High } & 5,3 & 7,1 & 6,2 \\\hline \text { Medium } & 2,5 & 5,4 & 2,3 \\\hline \text { Low } & 4,4 & 3,3 & 4,2 \\\hline\end{array}\end{array}$

-Refer to Table 10-1. The payoff table represents a:

A) prisoner's dilemma.
B) constant-sum game.
C) dominant strategy equilibrium.
D) sequential game.
E) price war.

Question 15

The following table lists the payoffs of two firms adopting three possible advertising strategies:
Table 10-5
$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Firm } 2\\\begin{array} { | c | c | c | c | } \hline \text { Firm 1 } & \text { High } & \text { Medium } & \text { Low } \\\hline \text { High } & 3,2 & 4,1 & 5,0 \\\hline \text { Medium } & 1,6 & 5,4 & 3,3 \\\hline \text { Low } & 0,4 & 5,5 & 6,2 \\\hline\end{array}\end{array}$

-Refer to Table 10-5. Identify the true statement.

A) Neither player has a dominant strategy.
B) Only Firm 1 has a dominant strategy.
C) Only Firm 2 has a dominant strategy.
D) Both firms have dominant-strategies.
E) The only equilibrium has both players using mixed strategies.

Question 16

A dominant strategy:

A) guarantees a player a higher payoff than its competitor.
B) calls for a contingent course of action.
C) is the best response to any strategy that the other player might select.
D) minimizes the other player's payoff.
E) sometimes means using a mixed strategy.

Question 17

A Nash equilibrium is defined as the outcome that:

A) results in equal payoffs to both players.
B) is unique and invariant to the strategy chosen by the other.
C) maximizes the sum of the players' payoffs.
D) results when both players lose by deviating from the equilibrium play.
E) maximizes each player's payoff against the strategy chosen by the other.

Question 18

Unlike a one-shot game, in a repeated game:

A) players have the opportunity to use mixed strategies.
B) each player's objective is to claim a greater payoff with the first move.
C) players have the opportunity to build trust and cooperation.
D) a player's prior reputation carries relatively little importance.
E) players are obliged to take independent actions.

Question 19

The following table shows the payoffs for Firm 1 and Firm 2 in a zero-sum game:
Table 10-2
$\begin{array}{c}\quad\quad\quad\text { Firm2}\\\begin{array}{|c|c|r|}\hline\text { Firm 1 } & \text { C1 } & {\text { C2 }} \\\hline \text { R1 } & 4,5 & 10,4 \\\hline \text { R2 } & 2,8 & 8,7\\\hline\end{array}\end{array}$


-Refer to Table 10-2. Identify the correct statement.

A) Firm 1's dominant strategy is R1.
B) The equilibrium strategies are R1 versus C2.
C) Neither player has a dominant strategy.
D) The equilibrium payoffs are 10 and 4.
E) The game is a constant-sum game.

Question 20

Which of the following is true of a zero-sum game?

A) The value of the game is equal to zero.
B) Each player always has a dominant strategy.
C) Each player's gain comes at the expense of the other.
D) There are only two players.
E) One player's payoff is independent of the other player's actions.

Question 21

Why is backward induction important in competitive strategy?

Question 22

The following table shows the payoffs for Firm 1 and Firm 2 in a zero-sum game:
Table 10-6
$\begin{array}{c} \quad \quad \quad \text { Firm 2 }\\\begin{array}{ | c | c | c | } \hline \text { Firm 1 } & \text { C1 } & \text { C2 } \\\hline \text { R1 } & 4 & 2 \\\hline \text { R2 } & 0 & 6 \\\hline\end{array}\end{array}$

-Refer to Table 10-6. The equilibrium strategies for Firm 1 and 2 are:.

A) R1 versus C2.
B) (.5R1, .5R2) versus (.5C1, .5C2).
C) (.75R1, .25R2) versus (.5C1, .5C2).
D) (.5R1, .5R2) versus (.75C1, .25C2).
E) The game is a constant-sum game.

Question 23

A mixed strategy:

A) involves two or more pure strategies, each with fixed probabilities.
B) is a course of action chosen by a player with certainty.
C) is a player's best response to any strategy that the other player might pick.
D) refers to the series of moves made by players in a repeated game.
E) is another term for a player's contingent actions.

Question 24

What is the dilemma in the prisoner's dilemma? What is the key assumption about behavior? Suggest one way to overcome the dilemma.

Question 25

List and explain the various forms of oligopolistic cooperation, which may benefit all firms, and lead to greater profitability.

Question 26

What is the role of information in a strategic game?

Question 27

How do constant-sum games and non-constant-sum games differ from each other? Give an example of each.

Question 28

List and briefly explain the main entry deterrence policies that an oligopoly firm might employ to prevent other firms from entering a market.

Question 29

Why is communication an important factor in competitive situations?

Question 30

Define the concept of Nash equilibrium. Why is it important?

Question 31

Define limit pricing. Under what conditions is it an optimal strategy?

Question 32

The payoff table shows the competition between a new entrant (Firm 1) and an incumbent firm (Firm 2). Determine each firm's equilibrium strategy.

Question 33

How does strategy formulation differ for zero-sum and non-zero-sum games?

Question 34

When is it optimal for players to adopt mixed strategies? What condition must an optimal mixed strategy satisfy?

Question 35

Discuss the role of reputation in strategic settings.

Question 36

How does finite competition differ from infinite competition between rival firms?

Question 37

Discuss the role of communication in a cooperative agreement.

Question 38

Which one of the following is not a feature of the tit-for-tat strategy?

A) Limited punishments for an opponent's defections.
B) A cooperative high-payoff equilibrium.
C) Perpetual punishments for an opponent's defections.
D) Neither firm has an incentive to be the first to defect.
E) The use of contingent strategies to resolve the prisoner's dilemma.

Question 39

What are the essential elements of a competitive situation (modeled as a game)?

Question 40

For the payoff table listed, determine the equilibrium outcome. Does either firm have a dominant strategy?

Question 41

Predatory pricing is a practice of deliberately pricing at a loss in order to bankrupt a rival.
(a) Is predatory pricing rational?

Question 42

Provide an example of a competitive situation where there is a second-mover advantage.

Question 43

Determine each player's equilibrium mixed strategy in the following non-zero-sum game.

Question 44

Determine all possible equilibrium outcomes in the following non-zero-sum game.

Question 45

Nintendo and Sony Playstation are each planning to introduce one new game into the market. Each is considering three different kinds of games: an urban action game like Grand Theft Auto, an adventure game like Tomb Raiders, or a strategy game like Sim City. The table shows each firm's profits (Sony's profit first) in millions of dollars:
(a) Assuming the firms act independently, find the equilibrium outcome. Briefly, explain your answer. Is this game an example of the prisoner's dilemma?

Question 46

Determine each player's equilibrium mixed strategy in the following non-zero-sum game.

Question 47

The payoff table below depicts price competition between two electronics stores. (Payoffs are weekly profits in thousands of dollars for each store.)
(a) The stores determine their strategies independently of one another. What are the stores' respective equilibrium strategies? Explain briefly.

Question 48

What do we mean by a first mover advantage? Why is it an important strategy? Give an example to illustrate your answer.

Question 49

Consider the following game: Two players must choose one of three options: rock, paper, or scissors. The winner is determined as follows: Paper slaps rock (and wins); rock crushes scissors (and wins); scissors cuts paper (and wins). If both players choose the same option, it results in a draw. Does the game have a dominant strategy? Does it have an optimal pure strategy?

Question 50

Construct a payoff table that depicts duopolists, each facing a kinked demand curve. With a kinked demand curve, all firms maintain the current price (at the kink in demand) unless conditions change drastically.

Question 51

Why does the strategy of tit-for-tat support cooperative equilibrium?