Consider a game between player A with a choice between moves d₁ and d₂, and player B with a choice between81 and 82, and the pay-offs given by:3₁Consider a zero-sum game with the following payoff matrix for player 1:61 62d₁ (4,6) (7,2)d₂ (2,8) (5,4)Is that game separable?a. Separable withr₁(d₁) = 5, r₁(d₂) = 2, 72(81) = 1, 72(82) = 4, (s₁ (d₁) = 2, 8₁ (d₂) = 4,82 (81) = 4, 82 (82) = 0b. Separable with a different solution that the ones proposedc.Separable withr₁(d₁) = 3, r1(d₂) = 3,(61) = 0, 72(82) = 1, (81 (d₁) = 1, 81 (d₂) = 4, 82 (81) = 5, 82 (82) = 2No, not separable.d.e.Separable withri (d₁) = 4, r₁(d₂) = 1, r2(81) = -1, 72(82) = 2, (81 (d₁) = 1, 81 (d₂) = 4, 82 (81) = 6, 82 (8₂) = 1f. Separable withr₁(d₁) = 4, r₁(d₂) = 2, 7₂(81) = 0,72(8₂) = 3, (s₁ (d₁) = 1, 8₁ (d₂) = 3, 82 (81) = 5, 82 (8₂) = 1Consider the payoff matrix M for a zero-sum game as defined below:81 82d₁0-2d₂-2-1M1 M₂ M3 M4 M5d₁ 0 1 5 6 8d₂ 10 652 3O a. r* = (1/2, 1/2), y* = (1/2, 1/2), V =0O b. r* = (0, 1), y* = (1/2, 1/2), [V| = 1/2O c. x =(2/3, 1/3), y* = (0, 1), V = 0O d. x* =(2/3, 1/3), y* = (2/3, 1/3), |V| = 4/3O e. r* = (1/3, 2/3), y* = (2/3, 1/3), |V| = 1/3O f. * = (1/3,2/3), y* = (1/3,2/3), [V| = 4/3O g. x* = (2/3, 1/3), y* = (1/3,2/3), [V| = 1/3Oh.Another answerPlayer 1 will play d₁ with probabilityThe two moves Player 2 needs to considering playing the most areprobabilitiesandThe value of the game is, and do with probabilityThe payoffs relate to player 1 who must choose between moves d₁ and d2, while player 2 has potential movesans 82.Find the optimal strategies x* and y* for players 1 and respectively. What is the value V of the game?and+with respectiveNote: you need to enter probabilities as numerical answers to 3 decimal places, not fractions. For example, if oneansweris 1/3, type 0.333. Also, for Player 2, make sure to mention to first mention their most likely move. We consider the following decision problem, with 4 decisions dį, i € {1, ... ,4}, and four possible outcomeswi, i E (1,...,4}, with the following table of profits:61 62 63 64d₁ 1 6 7 2d₂ 4 6 4 6d3 3 2 3 2d4 5 5 5 5According to optimism-pessimism rule, with degree of optimism a, :we should never choose decisionwe will choosewe will choosewe will chooseM1 M₂ M3 M4 M5d₁ 0 1 5 68d₂ 10 6 5 2 3+Consider a zero-sum game with the following payoff matrix for player 1:when a < 1/3;when 1/2 < a < 2/3;The value of the game is÷ when a > 3/4.Player 1 will play d₁ with probabilityandThe two moves Player 2 needs to considering playing the most areprobabilities, and d₂ with probabilityandwith respectiveNote: you need to enter probabilities as numerical answers to 3 decimal places, not fractions. For example, if oneansweris 1/3, type 0.333. Also, for Player 2, make sure to mention to first mention their most likely move.

Game theory is a tool used in economics by various business to make decisions. Decisions are taken…

Consider a game between player A with a choice between moves dj and d₂, and player B with a choice between 81 and 82, and the pay-offs given by: 81 82 d₁ (4,6) (7.2) d₂ (2,8) (5,4) Is that game separable? a. Separable with r₁(d₁) = 5,r₁(d) = 2, r2(61) = 1, 72(8₂) = 4, (81 (d₁) = 2, 81 (d₂) = 4, 82 (61) = 4,82 (8₂) = 0 b. Separable with a different solution that the ones proposed c. Separable with ri(di) = 3, r₁(d₂) = 3, 1(61) = 0,72(82) = 1, (81 (d₁) 1, 81 (d2) = 4,82 (81) = 5, 82 (82) = 2 No, not separable. d. e. Separable with ri (d₁) = 4, r₁(d₂) = 1,2(61) = -1, r2(82) = 2, (81 (d₁) 1, 81 (da) = 4,82 (81) = 6, 82 (8₂) = 1 f. Separable with r₁(d₁) = 4, r₁(d₂) = 2,72 (61) = 0, 72(8₂) = 3, (8₁ (d₁) = 1, 8₁ (₂) = 3, 82 (8₁) = 5, 82 (8₂) = 1

Consider a game between player A with a choice between moves dj and d₂, and player B with a choice between 81 and 82, and the pay-offs given by: 81 82 d₁ (4,6) (7.2) d₂ (2,8) (5,4) Is that game separable? a. Separable with r₁(d₁) = 5,r₁(d) = 2, r2(61) = 1, 72(8₂) = 4, (81 (d₁) = 2, 81 (d₂) = 4, 82 (61) = 4,82 (8₂) = 0 b. Separable with a different solution that the ones proposed c. Separable with ri(di) = 3, r₁(d₂) = 3, 1(61) = 0,72(82) = 1, (81 (d₁) 1, 81 (d2) = 4,82 (81) = 5, 82 (82) = 2 No, not separable. d. e. Separable with ri (d₁) = 4, r₁(d₂) = 1,2(61) = -1, r2(82) = 2, (81 (d₁) 1, 81 (da) = 4,82 (81) = 6, 82 (8₂) = 1 f. Separable with r₁(d₁) = 4, r₁(d₂) = 2,72 (61) = 0, 72(8₂) = 3, (8₁ (d₁) = 1, 8₁ (₂) = 3, 82 (8₁) = 5, 82 (8₂) = 1

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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