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

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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up
7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Caroline 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 Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 9 and Caroline will receive a payoff of 8. Caroline Left Right Left 8, 5 8. 7 Antonio Right 3, 6 9, 8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses and Caroline chooses
7. Solving for dominant strategies and the Nash equilibrium Suppose Rajiv and Simone 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 Rajiv chooses Right and Simone chooses Right, Rajiv will receive a payoff of 5 and Simone will receive a payoff of 5.
10. Player A and Player B are playing a game . First , Player A chooses to either " Keep " or " Pass " . Second , Player B observes A's choice and Player B then chooses to either Keep or Pass . This process continues which creates the sequential game below . Please mark decisions that rational and selfish players will choose at every decision node ( 3 decisions by player A and 3 decisions by player B ) - mark them on the Figure . What is the equilibrium of this game ?
7. Solving for dominant strategies and the Nash equilibrium Suppose Dmitri and Frances 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 Dmitri chooses Right and Frances chooses Right, Dmitri will receive a payoff of 7 and Frances will receive a payoff of 6. Frances Left Right Left 4, 3 6, 4 Dmitri Right 6, 7 7, 6 to choose The only dominant strategy in this game is for and Frances chooses The outcome reflecting the unique Nash equilibrium in this game is as follows: Dmitri chooses v
8. Solving for dominant strategies and the Nash equilibrium Suppose Tim and Alyssa 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 Tim chooses Right and Alyssa chooses Right, Tim will receive a payoff of 3 and Alyssa will receive a payoff of 6. Tim Left Left 5, 6 Right 4, 2 Alyssa Right 5,5 3,6 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Tim chooses and Alyssa chooses
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
4. David plays in a game where his strategy (set of possible choices) is denoted by x, which can be any integer between 1 and 7, against Goliath, whose strategy is denoted by y, which can be any integer between 1 and 7. David's and Goliath's utility functions are the same and given by: U(x, y) = (x-2)(y-2). Based on this information, determine whether each of the following statements are true or false. (a) The combination (x, y) = (2, 2) is a Nash equilibrium. (b) This game has no dominant strategy (a choice of integer that gives the highest payoff regardless of what the opponent chooses). (c) This game has only one dominated strategy (a choice of integer that would never be a best response to the opponent's choice of integer).
7. Solving for dominant strategies and the Nash equilibrium Suppose Gabriel and Nia 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 Gabriel chooses Up and Nia chooses Down, Gabriel will receive a payoff of 6 and Nia will receive a payoff of 4. Gabriel Up Down Up 6,3 3,3 Nia 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: Gabriel chooses and Nia chooses
7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah 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 Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses
Lee and Cody are playing a game in which Lee has the first move at A in the accompanying decision tree: Once Lee has chosen either aggression or cooperation, Cody, who can see what Lee has chosen, must choose either aggression or cooperation at B or C. Both players know the payoffs at the end of each branch. Lee chooses A Aggression Cooperation Cody chooses 8 Multiple Choice C Cody chooses Aggression aggression: aggression Cooperation Aggression In the equilibrium of this game, Lee chooses Cooperation aggression; cooperation -10 for Lee -10 for Cody 40 for Lee O for Cody O for Leo 40 for Cody 25 for Lee 25 for Cody and then Cody chooses.
5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A Up