3. A dominant strategy is a strategy that a. results in the highest payoff for all parties. b. has a higher payoff than alternative strategies some of the time and lower payoff than alternative strategies the rest of the time. c. has a lower payoff than any other strategy, no matter what the other player does d. has a higher payoff than any other strategy, no matter what the other player does

3. A dominant strategy is a strategy that a. results in the highest payoff for all parties. b. has a higher payoff than alternative strategies some of the time and lower payoff than alternative strategies the rest of the time. c. has a lower payoff than any other strategy, no matter what the other player does d. has a higher payoff than any other strategy, no matter what the other player does

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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1. Use the following one-shot, normal form game to answer the questions below. Strategy A 100, 125 300, 250 200, 100 250, 0 500, 500 750, 400 400, 300 -100, 350 0, -100 (a) Find each player's dominant strategy, if it exists. (b) Find the Nash equilibrium.
Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.
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Consider the attached payoff matrix:a. Does Player A have a dominant strategy? Explain why or why not.b. Does Player B have a dominant strategy? Explain why or why not.
Which of the following best describes a dominant strategy? Question 4Answer a. The strategy that a player chooses depends on what the other player does b. The strategy that a player chooses minimizes the other player's payoff c. The strategy that a player chooses is independent of what the other player does d. The strategy that a player chooses maximizes joint payoffs for both players
Use the following one-shot, normal-form game to answer the following questions a. Find each player’s dominant strategy, if it exists. b. Find each player’s secure strategy. c. Find the Nash equilibrium.
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
22. In order for a set of strategies to constitute a Nash Equilibrium a. Each player must adopt a dominant strategy b. Each player must adopt a mixed strategy c. Players must coordinate to adopt the set of strategies that will maximize their joint payoffs. d. Each player must adopt a strategy that results in the best outcome for the other player. e. Each player must adopt a strategy that is a best response to the strategies of the other players.
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.
6. Consider Jake and Al again. They are considering going to Portugal or Sweden once the pandemic ends. Here are their payoffs: Al's choices: Sweden Portugal Jake's choices (8, 4) (4, 9) Sweden (10, 5) Portugal (3, 6) and Al going to d) The strategy (P, S), represents Jake going to e) Is there a dominant strategy in this game? Explain. f) Find the Nash equilibrium (equilibria) in this game, if one or more exists.
2. B Left Right Up 1, 3 3, 1 A Down 2, 2 4, 4 a. Find the Nash equilibrium or equilibria b. Which player, if any, has a dominant strategy? с. Does A benefit from changing the game by reducing his or her payoff in this way?
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.