in every Nash equilibrium, the strategy of every player is a best response to the strategies chosen by the other players. (a) True. (b) False.
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in every Nash equilibrium, the strategy of every player is a best response to the strategies chosen by the other players.
(a) True. (b) False.
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- When the payoffs are profits, the maximin strategy selects the alternative or act with the maximum gain. True or False True FalseConsider the attached extensive-form game tree, where player 1 moves first, then player 2. The top payoff accrues to player 1, the bottom payoff to player 2. (a) Draw the strategic form for this extensive form game.(b) Find all of the Nash equilibria, including any mixed.(c) Which of these Nash equilibria do you think would be actually played? Why?Consider the following Guessing Game. There are n = 10 players simultaneously choosing a number in {1, 2, 3}. The winners are those closest to 1/2 the average guess (they evenly split the prize between the winners if there is more than one). Find the set of rationalizable strategy profiles. Justify your answer. please no handwriting and this course about game theory (topic Rationalizability) answer with all steps, please
- How is a Nash equilibrium outcome different from a rationalizable outcome? In a Nash equilibrium players are allowed to randomise. Rationalizable outcomes apply to dynamic games whereas Nash equilibrium does not. In a Nash equilibrium each player always has the correct conjecture about what the other player will do. Nash equilibrium only allows for unilateral changes in strategy. None of the above. No AnswerConsider the following game. Which one of the following statements is FALSE? 1. There are 7 subgames in this extensive-form game. 2. There are 6 proper subgames in this extensive-form game. 3. (BK, CE) is a Subgame Perfect Nash Equilibrium. 4. (BK, DE) is a Subgame Perfect Nash EquilibriumMr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 24 units of utility from a vote for their positions (and lose 24 units of utility from a vote against their positions). However, the bother of actually voting costs each 12 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Vote Vote Mrs. Ward Mr. Ward: -12, Mrs. Ward: -12 Don't Vote Mr. Ward: -24, Mrs. Ward: 12 The Nash equilibrium for this game is for Mr. Ward to payoff of Don't Vote Mr. Ward: 12, Mrs. Ward: -24 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of and for Mrs. Ward to units of utility. Under this outcome, Mr. Ward receives a
- Consider the two period Repeated Prisoner's Dilemma Game where each player is interested in the SUM of the payoffs she gets in each period. Players see the outcome after the play in each period. (The period payoffs are 10,5,1,0.) (i) Write out this game in its strategic form. (ii) Find all Nash equilibria and all Subgame Perfect Nash Equilibria.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 1,1Chris Evans (Don't Party, Stalk) Party Don't Party Find the Nash equilibrium for this simultaneous move game. (Party, Don't Stalk) (Don't Party, Don't Stalk) Paparazzo (Party, Stalk) Stalk 3,4 1, 1 Don't Stalk 4, 2 1,2
- Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.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.Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) None
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