Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 10, Problem 2CACQ
a
To determine
To find:The representation of game in normal form.
b)
To determine
To ascertain:The dominant strategy of players.
c)
To determine
To ascertain:The Nash equilibrium of game.
d)
To determine
To ascertain:Ranking of strategy pairs by aggregate payoffs.
e)
To determine
To ascertain:The outcome with the highest aggregate payoff.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In a two-player, one-shot, simultaneous-move game, each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. a. Write this game in normal form. b. Find each player’s dominant strategy, if it exists. c. Find the Nash equilibrium (or equilibria) of this game. d. Rank strategy pairs by aggregate payoff (highest to lowest). e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?
In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $500. If both players choose strategy B, each earns a payoff of $100. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $0 and player 2 earns $650. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $650 and player 2 earns $0.a) Write the above game in normal form.b) Find each player’s dominant strategy, if it exists.c) Find the Nash equilibrium (or equilibria) of this game.d) Rank strategy pairs by aggregate payoff (highest to lowest).e) Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?
Consider a game with two players A and B and two strategies X and Z. If both players play strategy X, A will earn $300 and B will earn $700. If both players play strategy Z, A will earn $1,000 and B will earn $600. If Player A plays strategy X and player B plays strategy Z, A will earn $200 and B will earn $300. If Player A plays strategy Z and player B plays strategy X, A will earn $500 and B will earn $400. Player B finds that:
a) strategy Z is a dominant strategy.
b) strategy X is a dominant strategy.
c) he has no dominant strategy.
d) strategy X is a dominated strategy.
e) strategy Z is a dominated strategy.
Chapter 10 Solutions
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
Knowledge Booster
Similar questions
- Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 4 7, 7 2, 6 B 10, 6 1, 7 12, 4 C 4, 6 8, 8 7, 7 D 1, 6 3, 9 6, 7arrow_forwardConsider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 7 7, 2 2, 6 B 5, 5 5, 4 8, 4 C 4, 6 8, 4 7, 5 D 1, 6 3, 5 6, 4 Highlight the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose E Has a dominant strategy to choose F Has a dominant strategy to choose G Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/F B/E B/G C/F C/G There is no pure strategy Nash…arrow_forwardConsider the following sequential move game played by three players, A, B and C. Player A moves first and chooses one of the following two payoff matrices, either Box 1 or Box 2. Following Player A's choice, Players B and C move simultaneously. Player B chooses one of two strategies, Top or Bottom, while Player C chooses one of two strategies, Left or Right. Player A; Box 1: Player B Player A; Box 2: Player B Top Bottom Top Bottom Player C Left 3,3,3 6,5,0 Player C Left 3,6,6 4, 10,0 Right 6,0,5 8, 1, 1 Right 4,0, 10 6,2,2 Each cell in the two boxes contains three numbers. The first number is the payoff to Player A, the second number is the payoff to Player B and the third number is the payoff to Player C. This implies that when choosing their respective strategies, Players B and C will consider the second and third payoff numbers respectively in each cell. Player A, of course, will focus on the first number in each cell in deciding which box to choose. What is the subgame perfect…arrow_forward
- Consider a sequential-move version of a rock-paper-scissor game. Players sequentially form one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. Suppose Player 1 moves first and Player 2 moves afterwards. In this game, what is the subgame perfect Nash equilibrium payoff of Player 1? 1 00 0-1arrow_forwardConsider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A/B), Player 2’s choices are shown in the column headings (C/D). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 C D A 8, 3 2, 4 B 7, 4 3, 5 Pick the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/C A/D B/C B/D There is no pure strategy Nash equilibrium for this gamearrow_forwardIn the game shown below, Players 1 and 2 are competing over how to divide up $100. Each player must move at the same time without knowledge of the other player’s move. The table shows the payoff for Player1 (Player 2’s payoff is $100 Player 1’s Payoff). Find the Nash equilibrium(s) for this game. That is, what strategy should Player 1 and Player 2 use for this game? If the Players use their optimal strategy, what will be the payoff for each player in this game? Player 2 Player 1 Left Middle Right Up 40 30 50 Middle 20 50 40 Down 30 20 30arrow_forward
- Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C), Player 2’s choices are shown in the column headings (D, E, F). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 D E F A 6, 8 4, 7 2, 9 B 2, 3 2, 6 4, 7 C 5, 4 7, 5 3, 6arrow_forwardConsider the following game: Player 1 chooses A, B, or C. If player 1 chooses A, the game ends and each player gets a payoff of $7. If player 1 chooses B, then player 2 observes their choice and plays X or Y. If player 1 chooses B and player 2 chooses X, the game ends. Player 1 gets a payoff of $14 and player 2 gets a payoff of $16. If player 1 chooses B and player 2 chooses Y, the game ends. Player 1 gets a payoff of $17 and player 2 gets a payoff of $14. If player 1 chooses Č, then player 2 chooses secretly to put either a $5 bill or a $20 bill into a sealed envelope. Player 1 does not observe his choice; rather she has two options: Open the envelope and gets whatever bill is inside. If she chooses this, player 2 gets nothing. Give the envelope back to player 2, and get $12 for sure. If she chooses this, player 2 gets the amount in the envelope. Draw the game tree for this game How many strategies does Player 1 have in this game?arrow_forwardAlice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $400. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium? a) never, since 800 > 400 b) when 400 > C and D > 800 but not when 800 > D c) whenever 400 > C d) when D > C and C > 400 e) whenever d < 800arrow_forward
- Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1’s actual move and then decides to move right or left. If player 1 moves right, player 1 receives $0 and player 2 receives $25. If both players move left, player 1 receives –$5 and player 2 receives $10. If player 1 moves left and player 2 moves right, player 1 receives $20 and player 2 receives $20. a. Write this game in extensive form. b. Find the Nash equilibrium outcomes to this game. c. Which of the equilibrium outcomes is most reasonable? Explain.arrow_forwardConsider the following strategic interaction between two players, Player 1 (P1) and Player 2 (P2). NOTE: The first number in each payoff pair noted below is P1's payoff and the second number is P2's payoff. P1 moves first and chooses between A and B. If P1 chooses B, the game ends, the payoffs are (3, 3). If P1 chooses A, then they play the following simultaneous move game: P2 D 1,4 1, 1 P1 G 2, 1 2, 4 Answer the following questions considering the whole game (starting with P1's choice between A and B as described above). i. This game has * subgames including the whole game itself. ii. Player 1 has e information sets and Player 2 has * information sets. ii. The Nash equilibrium of the last subgame is (are) O(F, C) O(F, D) OG, C) O(G, D) iv. The subgame perfect equilibrium of the whole game is(are) D(A/G, D) D(A/F, C) (B/G, D) O(B/G, C) O(B/F, C)arrow_forwardJohn and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -100). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -50 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -10). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Managerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning