Penalty point in soccer. Column Defend left Defend right Kick left 50, -50 80, 80 Row Kick right 90, -90 20, -20 Note that the payofts in each entry sum to zero, indicating that the players have diametrically opposed goals. Row wants to maximize his expec payoff, and column wants to maximize her expected payoff-which means she wants to minimize row's payoff. Which of the following strategy profiles are Nash Equilibria? Check all that apply. Kick Left, Defend Left Kick Left, Defend Right Kick Right, Defend Left Kick Right. Defend Right There is no Nash Equilibrium in Pure Strategies

Penalty point in soccer. Column Defend left Defend right Kick left 50, -50 80, 80 Row Kick right 90, -90 20, -20 Note that the payofts in each entry sum to zero, indicating that the players have diametrically opposed goals. Row wants to maximize his expec payoff, and column wants to maximize her expected payoff-which means she wants to minimize row's payoff. Which of the following strategy profiles are Nash Equilibria? Check all that apply. Kick Left, Defend Left Kick Left, Defend Right Kick Right, Defend Left Kick Right. Defend Right There is no Nash Equilibrium in Pure Strategies

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 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
. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
3. Solving for dominant strategies and the Nash equilibrium Suppose Charles and Dina 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 Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 3 and Dina will receive a payoff of 8. Dina Left Right Left 3,7 2,6 Charles Right 4,5 3,8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses
7. Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth 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 Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Andrew Left Right Left 8,4 5,4 Beth Right 4,5 6,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth chooses
Consider a Centipede game below. Player 1 moves first and he can choose either L or R. If player 1 chooses R; then Player 2 moves choosing either L or R and if he chooses R then Player 1 moves choosing either L or R and then finally player 2 moves. 1 R 2 R 1 R 2 R 9,9 L 2,0 0,4 6,2 4,8 a. Represent this game in a normal form b. Find all the Pure Strategy Nash equilibrium or equilibria c. Find all the Sub-game Perfect Nash Equilibrium of this game
Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 1 Player 2 Left Right Top 6 1 9 4 Bottom 2 4 5 3 where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. D) What is Player 1’s maximin strategy?E) What is Player 2’s maximin strategy?F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?
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
2. Consider the following 2 → 2 normal form games: In both games Player 1 (the row player) chooses either strategy A or strategy B. Player 2 (the column player) chooses simultaneously strategy A or B. The outcomes are defined by the following matrices. The first number in each cell indicates the payoff of Player 1, the second number (after the comma) indicates the payoff of Player 2. A B Game I A B 50X, 30X 10X, 10X 10X, 10X 30X, 50X Game II A A 110X, 30X B 10X, 10X B 10X, 10X 30X, 50X where X > 0 is a payoff scale parameter. (a) For both games: find all Nash equilibria in pure strategies, if any, and find the Nash equilibrium in mixed strategies. How would you describe this strategic interaction in the two games?
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 Felix and Janet 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 Felix chooses Right and Janet chooses Right, Felix will receive a payoff of 7 and Janet will receive a payoff of 4. Felix Left Right Left 6,3 3,3 Janet Right 6,4 7,4 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Felix chooses and Janet chooses
The following payoff matrix represents a simultaneous-move game between two players: Kay and Jack. Each player has two choices: Black or White. The first number in each cell is the payoff to Kay, and the second number is the payoff to Jack. Jay Black White 50, 30, Black 50 30 Кay 45, 40, White 30 50 Refer to the scenario above. Which is true? a. This game has a dominant strategy equilibrium. b. This game has two dominant strategy equilibria. c. This game has two Nash equilibria. d. This game has one Nash equilibrium.