Consider two players, P1 and P2, each can choose A or B. The payoff matrix as a result of theplayers' choices are listed below:P1(P1, P2) = (B,A)A(P1, P2) = (B, B)B(P1, P2) = (A, A)-25Identify the pure-strategy Nash equilibrium (P1, P2).There are multiple pure-strategy Nash equilibria.There is no pure-strategy Nash equilibrium.(P1, P2) = (A, B)35A25-35P235-45B-3545

The best response strategy is defined as the strategy which gives the player the maximum payoff…

Consider two players, P1 and P2, each can choose A or B. The payoff matrix as a result of the players' choices are listed below: P1 (P1, P2) = (A, B) (P1, P2) = (B,A) A (P1, P2) = (B, B) B Identify the pure-strategy Nash equilibrium (P1, P2). There are multiple pure-strategy Nash equilibria. There is no pure-strategy Nash equilibrium. O (P1, P2) = (A, A) -25 35 A 25 -35 P2 35 -45 B -35 45

Consider two players, P1 and P2, each can choose A or B. The payoff matrix as a result of the players' choices are listed below: P1 (P1, P2) = (A, B) (P1, P2) = (B,A) A (P1, P2) = (B, B) B Identify the pure-strategy Nash equilibrium (P1, P2). There are multiple pure-strategy Nash equilibria. There is no pure-strategy Nash equilibrium. O (P1, P2) = (A, A) -25 35 A 25 -35 P2 35 -45 B -35 45

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 2E

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Consider two players, P1 and P2, each can choose A or B. The payoff matrix as a result of the players' choices are listed below: P1 O (P1, P2) (A, A) O (P1, P2) = (A,A) O (P1, P2) = (A, A) A Identify the pure-strategy Nash equilibrium (P1, P2). (P1, P2) = (A, A) B There are multiple pure-strategy Nash equilibria. O There is no pure-strategy Nash equilibrium. -25 35 A 25 -35 P2 35 -45 B -35 45
Consider two players in the game-theoretic setting below: Player 2 Choice A Choice B Choice 20 |-30 A -20 30 Player 1 Choice |-30 40 B 30 -40 What is the (pure-strategy) Nash equilibrium? There are more than one (pure-strategy) Nash equilibria. O (P1, P2) = (A, B) is the only (pure-strategy) Nash equilibrium. O (P1, P2) = (A, A) is the only (pure-strategy) Nash equilibrium. O There is no (pure-strategy) Nash equilibrium. O (P1, P2) = (B, A) is the only (pure-strategy) Nash equilibrium. (P1, P2) = (B, B) is the only (pure-strategy) Nash equilibrium.
The strategies and payoffs are given in the table. The first number of each payoff pair in the matrix is the payoff of player P1, and the second is the payoff of player P2. P2 Strategies Left Right P1 Up (2, 4) (1, 3) Strategies Down (1, 6) (6, 5) Select each pair of actions that would be a Nash Equilibrium of the above game. Up, Left Down, Left Up, Right Down, Right
Describe the game and find all Nash equilibria in the following situation: Each of two players chooses a non-negative number. In the choice (a1, a2), the payoff of the first player is equal to a1(a2 - a1), and the payoff of the second player is equal to a2(1 – a1 – a2).
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, 6
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 (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…
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, 7
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), 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 game
Find the Nash Equilibria for each of the following 2x2 games (The left payoff value is associated with the strategies (1 or 2) while the right payoff value is associated with the strategies (A or B)): (a) (b) (c) (d) B 1 3,3 2 4,4 5,5 1 2 1 2 1 2 A 2,2 24 A B 2,5 0,3 4,0 -5,2 A 1,0 0,6 B 4,1 5,5 A B -1,-3 -3,2 -4,1 0,0
Which is the correct mixed strategy Nash equilibrium for the below game? A Confess (3,2) Doesn't (0,0) confess (1/3); (2/3) (2/5); (3/5) (1/2): (1/2) B Confess (1/4); (3/4) Doesn't confess (0,0) (2,3)
a) Find the Nash equilibria in the game (in pure and mixed strategies) and the associated payoffs for the players. b) Now assume that the game is extended in the following way: in the beginning Player 1 can decide whether to opt out (this choice is denoted by O) or whether to play the simultaneous-move game in a) (this choice is denoted by G). If Player 1 opts out (plays O) then both Player 1 and Player 2 get a payoff of 4 each and the game ends. If Player 1 decides to play G, then the simultaneous-move game is played. Find the pure-strategy Nash equilibria in this extended version of the game. (Hint: note that Player 1 now has 4 strategies and write the game up in a 4x2 matrix.) c) Write the game in (b) up in extensive form (a game tree). Identify the subgames of this game.
A payoff matrix is shown below. With the payoffs in each field indicated in the form (Player 1’s payoff, Player 2’s payoff). Player 2 Left Right Player 1 Up ($1, $1) ($2, $4) Down ($7, $8) ($3, $3) Which of the following is true? The only Nash Equilibrium is Player 1 playing ‘Up’ and Player 2 playing ‘Right’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Left’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Right’. None of the other answers provided are true.