Two players, Player 1 and Player 2, are playing a game with two possible strategies A and B. Profits for each possible outcome areshown in the following table. Answer which statement is correct:Player 2ABPlayer 1A2.2-1.5B5.-1-3,-5Select one:a. The equilibrium in mixed strategies is {(4/7, 3/7), (2/5, 3/5)}○ b. The equilibrium in mixed strategies is {(2/5, 3/5), (2/3, 1/3)}There are two Nash equilibrium in pure strategies: [5,-1] and [-1,5]C.d. There are two Nash equilibrium in pure strategies: [A,B] and [A,A]

The objective of the question is to determine the correct statement about the Nash equilibrium in…

Answered: Two players, Player 1 and Player 2, are…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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GAME Z Player A B1 A1 7, 13 A2 3,8 Player B B2 15, 10 9,16 A3 5,8 4,7 In Game Z (see table above), assuming players move simultaneously. Which of the following is true? Player A has a dominant strategy Player B has a dominant strategy Both players have dominant strategies O Neither player has a dominant strategy
Consider the three-player game shown. Player 1 selects a row, either a1, b1 or c1. Player 2 selects a column, either a2 or b2. Player 3 selects a matrix, either a3 or b3. The first number in a cell is player 1’s payoff, the second number is player 2’s payoff, and the last number is player 3’s payoff. Derive the strategies that survive the IDSDS.
Make sure you clearly write your name and submission:. 1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. • "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper -1 0 1 rock 0 paper 1 scissors -1 (a) Show that this game does not have a pure Nash equilibrium. 1 X 3 (b) Show that…
(A) Two California teenagers Bill and Ted are playing Chicken. Bill drives his hot rod south down a one-lane road, and Ted drives his hot rod north along the same road. Each has two strategies: Stay or Swerve. If one player chooses Swerve he loses face; if both swerve, they both lose face. However, if they both choose Stay, they are both killed. The payoffs for the game of Chicken are given in the table below. Bill is the row player and Ted is the column player. Stay Swerve Stay -3, -3 2, 0 Swerve 0, 2 1, 1 (i) Find all pure strategy Nash equilibria. (ii) Find the mixed strategy Nash equilibrium. (iii) What is the probability that both teenagers will survive? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…
Consider the following simultaneous-move game that represents the payoffs from different advertising campaigns (low, medium, and high spending) for two political candidates that are running for a particular office. The values in the payoff matrix represent the share of the popular vote earned by each candidate is given below. The equilibrium in dominant strategies Candidate A-low Candidate A-medium Candidate A-high Ois (low. low). O is (medium, medium). O is (high, high). O is (medium, high) O does not exist. Candidate B-low Candidate B-medium Candidate B-high 50, 50 60,40 80, 20 40, 60 50, 50 65, 35 20, 80 35,65 50, 50
Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 1 Strategy A B с 21, 5 13, 4 a. What is player 1's optimal strategy? D 25, 9 28, 11 Strategy A. Player 1 does not have an optimal strategy. O Strategy B. b. Determine player 1's equilibrium payoff. Player 2 E 18, 15 9, 18 F 12, 12 14, 16
A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
2. Consider the two-by-two bimatrix game listed below: Left Right (2,-2) (1,-1) Up Down (3,-3) (-1,1) where the player "Row" chooses the action "up" or "down" and the player "Column" chooses the action "left" or "right". Describe a mixed strategy Nash Equilibrium for this game.
Consider the game in the table below. What is firm A's payoff from their best response to Firm B choosing Down? Firm A Left Straight Right Up 7,5 3,7 1,3 Firm B Middle 8,14 2,7 4,17 Down 9,13 1,3 2,16 16
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()

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