Question 1

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.The symbol z is equal to ________,and the symbol t is equal to ________.

Accepted Answer

The scenario likely defines specific values for symbols z and t, where z is equal to 1 and t is equal to -1.

Question 2

A ________ is an extensive-form representation of a game.

Accepted Answer

A game tree is a graphical representation of a game that shows all possible sequences of actions and their outcomes. It is a useful tool to determine optimal strategies and outcomes in games. Payoff matrix is a table that shows the outcomes of a game based on the choices made by each player. Nash equilibrium is a solution concept in game theory where no player has an incentive to change their strategy given the strategies of the other players. Pure strategy refers to a specific set of actions chosen by a player in a game.

Question 3

Scenario: The ultimatum game is a two-player game played as follows. One player, the proposer, is told to divide a sum of money between the two players. The proposer proposes how to divide the sum. The other player, the responder, then chooses to either accept or reject the proposal. If the responder accepts the proposal, the money is split according to the proposal. If the responder rejects the proposal, neither receives any money. When this game is played by real people from a common social group, it is frequently observed that the proposer offers close to 50-50 split and the responder rejects offers below 30 percent of the sum.
-Refer to the scenario above.According to the theory presented in the textbook,if the proposer offered 0 percent,should the responder accept?

Accepted Answer

The answer of Scenario: The ultimatum game is a two-player...

Question 4

Refer to Evidence-Based Economics element in section 13.4 of the text.
a)Describe a variation of beauty contest game used in the experiment.
b)Explain why every player submitting 0 is the Nash equilibrium.
c)Describe the results of the experiment.

Accepted Answer

The answer of Refer to Evidence-Based Economics element in section...

Question 5

Scenario: The ultimatum game is a two-player game played as follows. One player, the proposer, is told to divide a sum of money between the two players. The proposer proposes how to divide the sum. The other player, the responder, then chooses to either accept or reject the proposal. If the responder accepts the proposal, the money is split according to the proposal. If the responder rejects the proposal, neither receives any money. When this game is played by real people from a common social group, it is frequently observed that the proposer offers close to 50-50 split and the responder rejects offers below 30 percent of the sum.
-Refer to the scenario above.According to the theory presented in the textbook,which of the following would happen in the Nash equilibrium?

Accepted Answer

In the Nash equilibrium of the ultimatum game, the proposer offers the smallest possible amount (close to 0 percent), and the responder accepts it, because receiving something is better than nothing.

Question 6

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.In this game,choosing a ________ has a clear advantage for the kicker,and choosing a ________ has clear advantage for the goalie.

Accepted Answer

The answer of Scenario: The following table represents the game...

Question 7

Scenario: Two friends are playing a game. The rules of the game are simple. Each player is given a bag containing a white ball and a black ball, and the two friends are asked to simultaneously draw one ball each. They are informed about their payoffs just before the game begins, which are shown in the matrix below. The first number listed in each cell is the payoff to the row player, and the second number listed is the payoff to the column player.
 
-Refer to the scenario above.Which of the following is true?

Accepted Answer

The answer of Scenario: Two friends are playing a game....

Question 8

The optimal strategy of a goalie in penalty kicking is similar to that in ________.

Accepted Answer

The optimal strategy of a goalie in penalty kicking is similar to that in a zero-sum game because in both scenarios, one player's gain is exactly equal to the other player's loss.

Question 9

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.This game ________.

Accepted Answer

The answer of Scenario: The following table represents the game...

Question 10

Scenario: Two friends are playing a game. The rules of the game are simple. Each player is given a bag containing a white ball and a black ball, and the two friends are asked to simultaneously draw one ball each. They are informed about their payoffs just before the game begins, which are shown in the matrix below. The first number listed in each cell is the payoff to the row player, and the second number listed is the payoff to the column player.
 
-Refer to the scenario above.Which of the following is true in this case?

Accepted Answer

There are three Nash equilibria in this game: (black, white), (white, black), and (white, white).

Question 11

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.This game is ________.

Accepted Answer

In a zero-sum game, one player's gain is exactly balanced by the other player's loss. In this scenario, if the kicker scores, the goalie loses, and if the goalie saves, the kicker loses, making it a zero-sum game for both players.

Question 12

Another game frequently played in MBA strategy classes is the acquire a company game.The set-up of the game is as follows.Company A has only one asset,offshore oil leases.The expected profit from these leases is uniformly distributed between $0 and $100 million,so the expected value to company A is $50 million.Company B is thinking of acquiring Company A.Company B's management is more efficient than A's; specifically,the value of A's assets under B's management is 1.5 times greater.For example,the expected value of A's oil leases under B's management is 1.5 $50 million,or $75 million.Company B can submit a written bid to acquire Company A.A will review the bid,and accept or reject the offer after learning the value of the oil leases with certainty.
You are advising Company B on its potential acquisition of Company A.What is the optimal bid for Company B to submit?

Accepted Answer

If Company B submits a bid, Company A will only accept if the bid is higher than the actual value of the leases. Since the value is uniformly distributed between $0 and $100 million, any bid will likely be accepted only when the value is higher than the bid, leading to a loss for Company B. Therefore, the optimal strategy is not to submit a bid.

Question 13

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.The symbol k is equal to ________,and the symbol j is equal to ________.

Accepted Answer

The answer of Scenario: The following table represents the game...

Question 14

Gary and Christine are two players in game in which Gary's decisions are based on the choice made by Christine.This is an example of a(n)________.

Accepted Answer

The given scenario describes an extensive-form game, which is a game in which players make decisions sequentially and the actions of one player affect the options available to the other player. It is not a simultaneous-move game as the players' decisions are not made simultaneously. It is not a pure-strategy game as there is no mention of the players choosing between multiple strategies. It is also not necessarily a zero-sum game as the outcome may not necessarily result in one player gaining exactly what the other player loses.

Question 15

Scenario: The ultimatum game is a two-player game played as follows. One player, the proposer, is told to divide a sum of money between the two players. The proposer proposes how to divide the sum. The other player, the responder, then chooses to either accept or reject the proposal. If the responder accepts the proposal, the money is split according to the proposal. If the responder rejects the proposal, neither receives any money. When this game is played by real people from a common social group, it is frequently observed that the proposer offers close to 50-50 split and the responder rejects offers below 30 percent of the sum.
-Refer to the scenario above.According to the theory presented in the textbook,if the proposer offered 1 percent,should the responder accept?

Accepted Answer

Accepting any positive amount of money is rational if the alternative is receiving nothing, as rejecting the offer results in both players receiving no money.

Question 16

Maria Brown is a young tennis player who has shot to fame after defeating Sarah Knowles in three consecutive matches.In the fourth match,Sarah decides to serve to the left each time.Is this an optimal winning strategy for Sarah?

Accepted Answer

The answer of Maria Brown is a young tennis player...

Question 17

Does game theory always predict real-world situations involving strategic interactions? Why or why not?

Accepted Answer

The answer of Does game theory always predict real-world situations...

Question 18

Scenario: The ultimatum game is a two-player game played as follows. One player, the proposer, is told to divide a sum of money between the two players. The proposer proposes how to divide the sum. The other player, the responder, then chooses to either accept or reject the proposal. If the responder accepts the proposal, the money is split according to the proposal. If the responder rejects the proposal, neither receives any money. When this game is played by real people from a common social group, it is frequently observed that the proposer offers close to 50-50 split and the responder rejects offers below 30 percent of the sum.
-Refer to the scenario above.According to the theory you learned in the textbook,if the proposer offered 50 percent,should the responder accept?

Accepted Answer

According to the scenario, it is frequently observed that the proposer offers close to a 50-50 split. Therefore, if the proposer offered 50 percent, this is a fair offer that the responder should accept because rejecting the offer would result in receiving nothing.

Question 19

Scenario: The following table represents the game matrix for the penalty kicks in a soccer game. There are two players in the game: the kicker and the goalie. The kicker has two choices: to kick the ball to the right or to the left. The goalie also has two choice to jump to the right, or to the left. Each goal counts to +1 point for the kicker and -1 points for the goalie. The symbols in the table stand for the numerical payoff to each player. The first symbol listed in each cell is the payoff to the kicker, and the second number listed is the payoff to the goalie.
 
-Refer to the scenario above.The symbol p is equal to ________,and the symbol w is equal to ________.

Accepted Answer

The answer of Scenario: The following table represents the game...

Question 20

Scenario: A common game played in many MBA-level classes on microeconomic theory and strategy is the dollar auction game. In this game, the professor takes on the role of auctioneer, offering to auction off a dollar bill to the highest bidder. This is an open-outcry auction, so students just shout out their bids. The one catch to the game is that the winning bidder pays her bid (the highest bid received), but the second-highest bidder must also pay the auctioneer the amount of her highest bid.
-Refer to the scenario above.In the dollar auction,what is your equilibrium bidding strategy?

Accepted Answer

The dollar auction is a classic example of a situation where rational behavior can lead to an undesirable outcome. In this game, the only way to win is to bid higher than everyone else, but the catch is that both the winning bidder and the second-highest bidder have to pay their respective bids. This means that if two players get caught up in a bidding war, they may end up paying much more than the value of the dollar bill. In fact, in theory, the bidding could go on indefinitely, with each player continuing to raise their bid in an attempt to avoid losing money. Therefore, the best strategy is to not bid at all and avoid getting caught up in the auction.

Quiz 13: Game Theory and Strategic Play

A ________ is an extensive-form representation of a game.

Refer to Evidence-Based Economics element in section 13.4 of the text. a)Describe a variation of beauty contest game used in the experiment. b)Explain why every player submitting 0 is the Nash equilibrium. c)Describe the results of the experiment.

The optimal strategy of a goalie in penalty kicking is similar to that in ________.

Gary and Christine are two players in game in which Gary's decisions are based on the choice made by Christine.This is an example of a(n) ________.

Maria Brown is a young tennis player who has shot to fame after defeating Sarah Knowles in three consecutive matches.In the fourth match,Sarah decides to serve to the left each time.Is this an optimal winning strategy for Sarah?

Does game theory always predict real-world situations involving strategic interactions? Why or why not?