Answered: 4. Find all correlated equilibria of…

4. Find all correlated equilibria of the "Bach or Stravinsky" game. What is the highest symmetric payoff that can be achieved? Can this payoff be achieved with a public signal?

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter13: Between Competition And Monopoly

Section: Chapter Questions

Problem 10DQ

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7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 6 and Aaliyah will receive a payoff of 4. Russell Up Down Aaliyah Up 6,3 3,3 Down 6,4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses and Aaliyah chooses
3. Two players play the following game for infinite times. Cooperate Betray Cooperate 10, 20 -25, 30 Betray 15, -23 -12, -19 For the player to continue to cooperate what would be the ranges of their discount factor, 8, and 82, respectively?
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1. Each of two players simultaneously announces either Rock, Paper, or Scissors. Paper beats Rock, Rock beats Scissors, and Scissors beats Paper. The player who names the winning object receives $1 from her opponent. If both players make the same choice, no payment is made. Each players's preferences are represented by by the expected amount of money she receives. a) Formulate the situation as a strategic game and find all its mixed strategy equilibria. Make sure that you consider all different supports. b) Find all the mixed strategy equilibria of the modified game in which player 2 is prohibited from announcing Rock.
4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.
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7. Solving for dominant strategies and the Nash equilibrium Suppose Van and Amy are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Van chooses Right and Amy chooses Right, Van will receive a payoff of 5 and Amy will receive a payoff of 4. Van Left Left 8,3 Right 5,3 Amy Right 4,4 5,4 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Van chooses and Amy chooses
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3. For the friend-foe game, recall that there were 3 Nash equilibria possible, but the equilibria set didn't include the cooperative outcome, for which both players would win. Friend Foe Friend | 500,500 0,1000 Foe 1000,0 0,0 a) If the game is played repeatedly, propose a play strategy that will enforce cooperation. For what values of ô (discount factor) the equilibrium will be (Friend, Friend)?
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1. Use the following game tree to answer parts a & b. At a chance node (Nature's turn) or when a player is indifferent between strategies, each branch has equal likelihood (50% chance they take either path). Nature receives no payoff. Assume players are mistake proof. Use a complete strategy when discussing the results of this game and provide a payoff, even if that payoff is an expected one. Recall that an expected payoff is the "average" payoff: for example if with 50% chance we receive a payoff of 5 and with 50% chance we receive a payoff of 2, the expected payoff is .5 x 5+ .5 x 2 = 3.5 a. What is the outcome of the game? Assume players are risk neutral (i.e., they see no difference in getting a payoff of 5 vs an expected payoff of 5). Red 0, 1, 3, 3 3, 2, 3, 2 Dorothy Blue Top 1, 4, 3, 2 Scarecrow 50% Green Nature Right Bottom 0, 2, 3, 1 Lion 50% 1, 3, 4, 2 3, 4, 3, 2 50% Left Nature 3, 2, 1, 2 Up 50% Red. 1, 3, 4, 2 Down Tinman Blue 0, 3, 3, 3 Yellow Dorothy 4, 3, 4, 2…