Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Question
Chapter 10.1, Problem 17E
(A)
To determine
The saddle value of the matrix game
(B)
To determine
To calculate: The optimal strategies of matrix game
(C)
To determine
To calculate: The value of the game of the matrix game
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2. Give an example of a 2-player, zero-sum game with the following properties (by
giving its payoff matrix from the perspective of the row player):
• The row player has strategy set {1, 2} and the column player has strategy set
{C1, C2}
• The security levels of r₁, r2, C1, and c₂ are respectively −1, −2, 4, and 3.
2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 10.1 - Suppose that a and k are both saddle values of the...Ch. 10.1 - Repeat Example 1 for the HDTV game matrix...Ch. 10.1 - Determine which of the matrix games below are...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...
Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - For the matrix game of Problem 31, would you...Ch. 10.1 - For the matrix game of Problem 32, would you...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - Is there a value of m such that the following is...Ch. 10.1 - Prob. 42ECh. 10.1 - Price war a small town on a major highway has only...Ch. 10.1 - Investment Suppose that you want to invest $10,000...Ch. 10.1 - Store location two competitive pet shops want to...Ch. 10.1 - Store location Two competing auto parts companies...Ch. 10.2 - Let M=abcd (A) Show that if the row minima belong...Ch. 10.2 - (A) Using Theorem 4, give conditions on a,b,c, and...Ch. 10.2 - Solve the following version of the two-finger...Ch. 10.2 - Solve the matrix game: M=112324113Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - You R and a friend C are playing the following...Ch. 10.2 - You R and a friend C are playing the following...Ch. 10.2 - For M=abcdP=p1p2Q=q1q2 Show that PMQ=EP,QCh. 10.2 - Using the fundamental theorem of game theory,...Ch. 10.2 - Show non strictly that the determined solution...Ch. 10.2 - Show that if a 22 matrix game has a saddle value,...Ch. 10.2 - Explain how to construct a 22 matrix game M for...Ch. 10.2 - Explain how to construct a 22 matrix game M for...Ch. 10.2 - In Problems 47 and 48, derive the formulas of...Ch. 10.2 - In Problems 47 and 48, derive the formulas of...Ch. 10.2 - Bank promotion A town has only two banks, bank R...Ch. 10.2 - Viewer ratings A city has two competitive...Ch. 10.2 - Investment You have inherited $10,000 just prior...Ch. 10.2 - Corporate farming For a one-time play...Ch. 10.3 - Show that M=1132 is a strictly determined matrix...Ch. 10.3 - Solve the following matrix game using geometric...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - Is there a better way to solve the matrix game in...Ch. 10.3 - Is there a better way to solve the matrix game in...Ch. 10.3 - Explain why the value of a matrix game is positive...Ch. 10.3 - Explain why the value of a matrix game is negative...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In the Problems 1722, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In the Problems 1722, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In Problems 23 and 24 remove recessive rows and...Ch. 10.3 - In Problems 23 and 24 remove recessive rows and...Ch. 10.3 - (A) Let P and Q be strategies for the 22 matrix...Ch. 10.3 - Use properties of matrix addition and...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.4 - Outline a procedure for solving the 45 matrix game...Ch. 10.4 - Suppose that the investor in Example 1 wishes to...Ch. 10.4 - In Problems 1-4, solve each matrix game 140012Ch. 10.4 - In Problems 1-4, solve each matrix game. 112201Ch. 10.4 - In Problems 1-4, solve each matrix game. 012103230Ch. 10.4 - In Problems 1-4, solve each matrix game. 120012201Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - Scissors, paper ,stone game This game is well...Ch. 10.4 - Player R has a $2, a $5,and a $10 bill. Player C...Ch. 10.4 - Headphone sales. A department store chain is about...Ch. 10.4 - Tour agency A tour agency organizes standard and...Ch. 10 - In Problems 1 and 2, is the matrix game strictly...Ch. 10 - In Problems 1 and 2, is the matrix game strictly...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Delete as many recessive rows and columns as...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - Does every strictly determined 22 matrix game have...Ch. 10 - Does every strictly determined 33 matrix game have...Ch. 10 - Finger game Consider the following finger game...Ch. 10 - Refer to Problem 29. Use linear programming and a...Ch. 10 - Agriculture A farmer decides each spring whether...Ch. 10 - Agriculture Refer to Problem 31. Use formulas from...Ch. 10 - Advertising A small town has two competing grocery...Ch. 10 - Advertising Refer to Problem 33. Use linear...
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