Finite Mathematics & Its Applications, Books A La Carte Edition (12th Edition)
12th Edition
ISBN: 9780134464039
Author: Goldstein, Larry J.; Schneider, David I.; Siegel, Martha J.; Hair, Steven
Publisher: PEARSON
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Chapter 9.3, Problem 2CYU
(a)
To determine
To calculate: The optimal strategy for C for the game having payoff matrix
(b)
To determine
The optimal strategy for C for the game having payoff matrix
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Find the optimal strategies, P and Q, for the row and column players, respectively.
−2
−5
−8
−4
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 =
Calculate the expected payoff of the game with payoff matrix
P =
2
0
−2
2
−1
0
0
−2
−2
0
0
1
3
1
−1
2
using the mixed strategies supplied. HINT [See Example 1.]
R = [0 0 0 1], C = [0 0 1 0]T
Find the saddle point of the game given by the payoff matrices A below.
Chapter 9 Solutions
Finite Mathematics & Its Applications, Books A La Carte Edition (12th Edition)
Ch. 9.1 - Solutions can be found following the section...Ch. 9.1 - Prob. 2CYUCh. 9.1 - Prob. 3CYUCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 7E
Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 112, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - For each of the games that follow, give the payoff...Ch. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.2 - Solutions can be found following the section...Ch. 9.2 - Prob. 2CYUCh. 9.2 - Prob. 1ECh. 9.2 - Suppose that a game has payoff matrix [102120011]...Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Flood Insurance A small business owner must decide...Ch. 9.2 - 7. Two players, Robert and Carol, play a game with...Ch. 9.2 - Rework Exercise 7 with [.7.3] as Roberts strategy.Ch. 9.2 - Two players, Robert and Carol, play a game with...Ch. 9.2 - 10. Rework Exercise 9 with as Robert’s...Ch. 9.2 - 11. Assume that two players, Renée and Carlos,...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - 16. Three-Finger Morra Reven and Coddy play a game...Ch. 9.3 - Prob. 1CYUCh. 9.3 - Prob. 2CYUCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Exercises 5–12, determine the value of the game...Ch. 9.3 - In Exercises 512, determine the value of the game...Ch. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - In Exercises 13–16, determine the value of the...Ch. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Football Suppose that, when the offense calls a...Ch. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Three-Finger Mor ra Reven and Coddy play a game in...Ch. 9.3 - Advertising Strategies The Carter Company can...Ch. 9 - 1. What do the individual entries of a payoff...Ch. 9 - Prob. 2FCCECh. 9 - Prob. 3FCCECh. 9 - Prob. 4FCCECh. 9 - Prob. 5FCCECh. 9 - Prob. 6FCCECh. 9 - Prob. 7FCCECh. 9 - What is meant by the optimal mixed strategies of R...Ch. 9 - In Exercises 14, state whether or not the games...Ch. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6P
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- The payoff matrix for a game is 4 3 3 0 2 0 −2 0 2 . Compute the expected payoffs of the game for the pairs of strategies in parts (a–d). (Round your answers to two decimal places.) (a) P = 1 3 1 3 1 3 , Q = 1 3 1 3 1 3 E = (b) P = 1 4 1 2 1 4 , Q = 1 8 3 8 1 2 E = (c) P = .4 .3 .3 , Q = .6 .2 .2 E = (d) P = .1 .5 .4 , Q = .3 .3 .4 E =arrow_forwardThe payoff matrix for a game is given by 1 −4 −4 2 . Compute the expected payoffs of the game for the pairs of strategies in parts (a–d). (Round your answers to one decimal place.) (a) P = 1 0 , Q = 1 0 E = (b) P = 0 1 , Q = 1 0 E = (c) P = 1 2 1 2 , Q = 1 2 1 2 E = (d) P = 0.6 0.4 , Q = 0.1 0.9arrow_forwardQ1-) Analyze payoff matrix below. a-) Consider the grim trigger strategy for the game? Analyze the conditions for which this strategy constitutes an subgame perfect equiillbria. b-) Analyze the conditions for the tit for tat strategy to be equilibrium for the following histories: Histories that ends with (C,C) and (C,D) NOTE a = 1 h = 7arrow_forward
- You are involved in making one of three possible decisions in your company. There are four states of nature that are being considered. The payoffs and losses appear in the following matrix. Decisions State Nature 1 State Nature 2 State Nature 3 State Nature 4 Maximin Decisions Payoffs? Decision 1 40 -20 10 -2 Decision 2 -10 30 -5 20 Decision 3 0 60 10 -40 Assume you estimate the probabilities of the states of nature to be as follows: P(N1) = .6 P(N2) = .2 P(N3) = .1 P(N4) = .1 Under these conditions which decision would you choose: D1, D2, or D3? Now assume that probabilities on the states of nature cannot be estimated. This makes the issue one of “decision making under uncertainty.” If you want to use the Maximin Strategy (maximizing your…arrow_forwardThe payoff matrix for a game is given by 1 −1 −1 3 . Compute the expected payoffs of the game for the pairs of strategies in parts (a–d). (Round your answers to one decimal place.) (a) P = 1 0 , Q = 1 0 E = (b) P = 0 1 , Q = 1 0 E = (c) P = 1 2 1 2 , Q = 1 2 1 2 E = (d) P = 0.7 0.3 , Q = 0.2 0.8 E =arrow_forwardA small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with pmf x 1 2 3 4 5 6 p(x) 1/5 2/15 3/15 4/15 3/15 2/15 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00.If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]arrow_forward
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