Find the optimal strategies, P and Q, for the row and column players, respectively. -5 3 -8 P = Q = Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E =
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- Which of the following is FALSE for the grim trigger strategy and the infinite horizon repeated Prisoner's Dilemma game illustrated above? A. In the grim trigger strategy profile, if a player chooses D in a period, then both players chooses D forever after that period B. The threshold discount factor for sustaining cooperation under grim trigger strategy depends on the utility numbers in the stage game C. If all utility numbers remain the same but 3 is replaced by 5 in the stage game, then cooperation CANNOT be sustained in this game for all possible values of the discount factor.Determine how much you would be willing to pay for the privilege of moving first in these two different games*1 1. There are two players, you and a rival. The player announcing the larger positive integer gets a payoff of $10, while the other player gets $0. 2. There are two players, you and a rival. The player announcing the smaller positive integer gets a payoff of $20, while the other player gets $2.The standard assumption of self-interest implies that in the dictator games with $10 endowment, the dictator should share (A) $0; (B) $2; (C) $5; (D) $10.
- 10) Consider a repeated game in which the following one-shot game between two players is repeated "infinitely." Denote by "d" the discount factor. (Assume both players have the same discount factor.) Player 2 Cooperate Defect Player 1 Cooperate 5, 4 0, 5 Defect 6, 0 1, 1 The two players try to support cooperation by using "grim trigger strategy" as discussed in class. Answer YES or NO to each of the following three questions. (a) Can they support cooperation if the common discount factor, d, is equal to 0.23? (b) Can they support cooperation if the common discount factor, d, is equal to 0.4? (c) Can they support cooperation if the common discount factor, d, is equal to 0.15?Two players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Select one: a. A trigger strategy will never support (A,A) as an equilibrium b. A tit-for-tat strategy will never support (A,A) as an equilibrium c. A tit-for-tat strategy will support (A,A) as an equilibrium if δ > 0.7 d. A trigger strategy will support (A,A) as an equilibrium if δ > 0.7Given the stage game above/below. Suppose that the players play (C,C) in period t = 1; 3; 5; ::: and plays (D,D) in period t = 2; 4; 6; ::. Compute the discounted payoff of each player.
- Economic development is a zero-sum game: if some people in market economies are able to get wealthy, they must be able to do so only if they are stealing from the rest of the population, and therefore the rest of the population must become poorer. Group of answer choices True FalseAssume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $2 and Player B gets $4. If Player A plays UP and Player B plays RIGHT then Player A gets $3 and Player B gets $6. If Player A plays DOWN and Player B plays LEFT then Player A gets $5 and Player B gets $2. If Player A plays DOWN and Player B plays RIGHT then Player A gets $1 and Player B gets $1. What is the mixed strategy expected payout for Player B? 1 40/15 39/15 11/2Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S (utility possibility frontier)?
- In the film Batman the Joker proposes a prisoner's dilemma. There are two ships A and B. The ships can either cooperate or detonate. The matrix of the model is: C. D C. 2,2 2,1 D 1,2 0,0 Assuming that players play this game infinitely repeatedly, so that after every round the probability that the game is repeated is m with 0 ≤ m ≤ 1. Devise at least two strategies that can be played in this indefinitely repeated game, find their expected payoffs, and find its Nash Equilibrium/Equilibria and the Subgame Perfect Nash Equilibria assuming that only available strategies are the ones you devised. Summarise the main insights from your analysis of the modified gameA strategy that a player will pursue regardless of any other player's decision is called _________. Question 10 options: game theory. collusion. prisoner's dilemma. dominant strategy.You are given the payoff matrix below. B1 B2 B3 A1 1 Q 6 A2 P 5 10 A3 6 2 3 a. Determine the range of values of P and Q in order for Player A to choose strategy A2 and PlayerB to choose strategy B2.b. Solve the problem in the perspective of the opponent. Are the ranges the same?c. What are the values of the game for (a) and (b)?