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

See similar textbooks

Similar questions

Consider the following sequential move game of imperfect information. Consider the following sequential move game of imperfect information. In the event that Otis chooses Down, then they play the simultaneous move game shown in normal form (where Otis chooses between X and Y and Maeve simultaneously chooses between W and V). A (25,6) Maeve Up B (5,10) (12,5) Otis Middle Maeve Down w Otis (0, 0) (10, 10) Y (15, 15) (0, 0) Find all (pure strategy) subgame perfect Nash equilibria.
Terry's payoff is the first number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [Select ] v and Kerry will [ [ Select ]
Consider the following game in extensive form, involving the chance parameter p. PT] =P (0,0) N Answer: U P[H] = 1-p h B P[T] = P h d (-60,60) (20,-20) (40,-40) t (0,0) N P[H] = 1-p (0,0) Suppose that p = 0.75 and the strategy profile (u, h) is played. What expected payoff does player B receive? (Report your answer in decimal form, rounding if necessary to two places.
1. Consider the following game in the normal form R 1,2 -1,2 3,2 1,5 M 1,1 2,-1 4,5 1,3 3.4 0,1 5,4 4,1 B 1,-1 N 4,4 6,1 1,4 a) Find the mixed strategy that dominates M b) Find the set B2 c) Find all the Pareto efficient strategy profiles
Please select the correct option and write clear. Thank you.
1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1
Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?
Construct the normal representation and the fully reduced normal representation of the game shown in Figure 1. 0 (0.5) (0.5) 1.r 1.s W1 X1 y1 Z1 0,0 2.t 2.t 0,4 a2 b2 a2 b2 Figure 1: Extensive-form game 2,-2 -2,2 -2, 2 2,-2
Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).
7
In the table below are the values of the ordinal utility function. Find all Nash equilibria of the game determined by the matrix below? Which of these are strict Nash equilibria?
= a) Suppose x 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? b) Suppose x = 4 and y = 3. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? c) Suppose x = 4 and y = 3. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game? d) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 1? e) Suppose x = 4 and y = 11. After all strategies that are dominated by a pure strategy are iteratively deleted for both players, how many strategies remain for Player 2? f) Suppose x = 4 and y = 11. What is the sum of both players' payoffs in all pure strategy Nash equilibria of the game?