Consider the following sequential-move game:This game involves three players, each making sequential decisions. The game proceeds asfollows:• Player 1 initiates the game by choosing between two actions: Left and Right.• Depending on Player 1's choice, Player 2 then decides, choosing between two actions,left (I) and right (`r`).• Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and`b`.The payoffs are determined by the sequence of choices made by all three players. Eachpayoff is represented by the triplet (x,y,z), where x, y, and z denote the payoffs for Player 1,Player 2, and Player 3, respectively. For example, if Player 1 chooses 'Left', Player 2 chooses'I', and Player 3 chooses `a` the resulting payoff would be (3,1,2). This indicates that Player1 receives a payoff of $3, Player 2 receives a payoff of $1, and Player 3 receives a payoff of$2 for this particular sequence of actions.LeftPlayer 2Player 1RightPlayer 2Player 3Player 3Player 3Player 33,1,27,4,1 0,3,97,3,1 5,6,70,0,1 1,6,40,4,8Find the backward-induction equilibrium of this game.

Nash equilibrium, named after the mathematician and economist John Nash, is a concept in game theory…

This game involves three players, each making sequential decisions. The game proceeds as follows: Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and 'b'.

This game involves three players, each making sequential decisions. The game proceeds as follows: Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and 'b'.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

QUESTION 12 This is a HOT SPOT question. You will need to evaluate the picture of the game below, and answer the question by clicking on a specific area (the hot spot) of the picture. Question: Are there any dominant strategies in this game? If there are, click on the box that corresponds to that dominant strategy (either UP, DOWN, LEFT, or RIGHT). If there aren't any anywhere outside of these boxes. If there are dominant strategies for both players, clicking on only one of them will suffice. Player 1 Player 2 Selected Coordinates Clear UP DOWN LEFT 45, 80 70, 100 RIGHT 50, 150 60, 60
Refer to Table Left-Right-ZigZag. How many pure strategy Nash equilibria does this game have? Table: Left-Right-ZigZag Player 1 Drive left Driver right Zigzag 1) 1 2) 2 3) 3 4) 4 5) None of the above. Drive left (1,1) (-1,-1) (0,0) Player 2 Driver right (-1,-1) (1,1) (0,0) Zigzag (0,0) (0,0) (0,0)
Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.
1
Player 1 and player 2 are playing a simultaneous-move one-shot game, where player 1 can move "up" or "down" and player 2 can move "left" or "right" The payoffs for the game are shown in the payoff matrix. The first number of each cell represents player 1's payoff, and the second number is player 2's. Use the matrix to answer the questions below. Player 1 2nd attempt Part 1 Part 2 Which of the following outcomes is a pure strategy Nash equilibrium of this game? P = (1-P) = Up Down Part 3 9= Left -16, -18 -20,7 Choose one or more: A. There is no pure strategy Nash equilibrium in this game. OB. Player 1 plays up; player 2 plays left. OC. Player 1 plays up; player 2 plays right. □ D. Player 1 plays down; player 2 plays left. O E. Player 1 plays down; player 2 plays right. Player 2 Suppose player 1 assigns probability p to playing up and (1 - p) to playing down. What do p and (1-p) have to be such that player 2 is indifferent between playing left and right? Round all answers to two decimal…
Tyler and Pam are arrested and charged with armed robbery. The police interview both suspects separately about their involvement in the crime. Each suspect has to make a decision. They can betray the other suspect by confessing that they both committed the crime, or they can cooperate with the other suspect by remaining silent. The table shows the sentences that Tyler and Pam will receive given their choices. Use the table to answer the question. What will be the dominant strategy outcome for Tyler and Pam? They both get 10 years. Pam gets 5 years, and Tyler gets 15 years. O They both get 12 years. O Tyler gets 5 years, and Pam gets 15 years. Tyler Stay silent Confess Stay silent Pam gets 10 years Tyler gets 10 years Pam gets 15 years Pam Tyler gets 5 years Confess Pam gets 5 years Tyler gets 15 years Pam gets 12 years Tyler gets 12 years
the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O
7
Keith and Blake play a simultaneous one-shot game. Keith chooses between Top and Bottom, whereas Blake chooses between left and right. Payoffs are given by (Keith's payoffs are listed first and Blake's payoffs second): Top+left: 3,-6. Top+right:0,-7 Bottom+left:4,0. Bottom+right:-2,6. In a mixed strategy equilibria, Keith will play Top with what probability? 1. 6/7 2. 1/4 3. 1/2 4. 1/7 5. 0 6. 3/4