Consider the game shown in Figure 3. Let A denote the probability that player 1 plays a, B the probability that player I plays b, C the probability that player 1 plays c, and D the probability that player 1 plays d. For player 2 X denotes the probability that player 2 plays x, Y that he/she plays y, and Z that he she plays z. Figure 3 Player 2 x y z a 3,7 4,6 5,4 Player 1 b 5,1 2,3 1,2 c 2,3 1,4 3,3 d 4,2 1,3 6,1 In a NE what is: b. C. d. C, the probability that player 1 plays c Z, the probability that player 2 plays z D, the probability that player 1 plays d X, the probability that player 2 plays x A, the probability that player 1 plays a

Consider the game shown in Figure 3. Let A denote the probability that player 1 plays a, B the probability that player I plays b, C the probability that player 1 plays c, and D the probability that player 1 plays d. For player 2 X denotes the probability that player 2 plays x, Y that he/she plays y, and Z that he she plays z. Figure 3 Player 2 x y z a 3,7 4,6 5,4 Player 1 b 5,1 2,3 1,2 c 2,3 1,4 3,3 d 4,2 1,3 6,1 In a NE what is: b. C. d. C, the probability that player 1 plays c Z, the probability that player 2 plays z D, the probability that player 1 plays d X, the probability that player 2 plays x A, the probability that player 1 plays a

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3:51 9 M 23 The mixed strategy Nash equilibrium of the following * game is Player 2 R. L Player 1 U 2,2 3,1 D 3.-1 0.0 U with 3/4 probability and D with 1/4 probability for player 1; L with1/2 probability and probability for player 2 with 1/2 U with 1/2 probability and D with 1/2 probability for player 1; L with1/4 probability and R with 3/4 probability for player 2 U with 1/4 probability and D with 3/4 probability for player 1; L with1/2 probability and R with 1/2 probability for player 2 O None of the above. U with 1/2 probability and D with 1/2 probability for player 1; L with3/4 probability and R with 1/4 probability for player 2
3. Consider the game below. С1 C2 C3 R1 1, 1 4, 6 8, 5 1, 2 5, 4 R2 R3 2, 6 2, 7 7, 6 0, 7 3.1. Does the game have any pure strategy NEs? 3.2. Check whether a mixed strategy NE exists in which A is mixing R1 and R2 with positive probabilities, playing R3 with zero probability, while B is mixing C1 and C3 with positive probabilities while playing C2 with zero probability. [Let (p1,P2, P3) be the probabilities with which A plays (R1, R2,R3) and let (q1,92, 93) be the probabilities with which B plays (C1, C2,C3). Make use of the following NE test: m* is a NE if for every player i, u;(mị , m²¿) = u;(Si, m²¡) for every si E S¡|m¡(sji) > 0 and u¡(m¡ ,m²¡) > u¡(s¡,m;) for every si E S¡ |m¡ (s¡) = 0. Hint: Each player must be indifferent between those of her pure strategies that are used (with positive probability) in her mixed strategy, and unused strategies must not yield a payoff that is higher than the payoff a player gets with her NE (mixed) strategy.] %3D
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in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working!!!!!!!
For the game given, find a Nash equilibrium in which both players randomize.
5 players must simultaneously choose a number from the interval [0, 9]. Let xi denote the number chosen by player i; x = (x1, . . . , x5) all the selected numbers; x−i = x\xi all the selected numbers except the one chosen by player i. If player i chooses the number xi ∈ [0, 9], while the others choose numbers x−i, then the utility of player i is given by ui(xi, x−i) = 4(9 − xi) + 2Σ5 j=1 xj. Find the Nash equilibrium of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game, obligating them to choose the number 9?
.What is the probability of getting a king if a card is drawn from a pack of 52 cards?
7. N [0.75] B A [0.25] 1 E F 6 2 J K J K 12 3 9. 6 6. 1 In equilibrium, what is the probability that player 1 will use the pure strategy E in this game?
2. Consider the following two player game in normal form: Player 2 R 0, 5 2, 3 2, 3 Player 1 M 2, 3 0, 5 3, 2 B 5,0 3, 2 2, 3 (a) Show that for Player 1, strategy T is strictly dominated by a mixed strategy in which actions M and B are played with positive probability. (b) Find a mixed strategy Nash equilibrium of this game. 352
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