Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Textbook Question
Chapter 11.3, Problem 20E
In Problem 17-20, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.
If a matrix game is fair then some payoffs are positive and some are negative.
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(b) Consider the following pay-off matrix of a 2 x 2 game.
player B
4
player A
-4
-4 4
How will you solve this game?
ANswer all
1. Below is the Boeing-Airbus Game in the absence of any government policy. Suppose both governments subsidize their own producers by paying 25 if the firm enters.a. Redraw the game matrix to reflect the new payoffs.b. Find all Nash equilibria of the new game.
c. What are the welfare effects in each country, when both governments subsidize their own producer?
PRODUCE
DON’T PRODUCE
produce
-5,-5
100,0
don’t produce
0,100
0,0
Consider the following game. Players 1 and 2 are partners in a firm. If they both invest 10 ina project, the project will achieve an income of 13 per person, so both will get net earningsof 3. If only one of them invests, the project earns only 5 per person, leading to a payoff of-5 for the person who invested and 5 for the other. If none of them invests, both get nothing.They can only choose to invest 10 or not invest at all.
1. Write down the payoff matrix of the game.2. Assume that both players only care about their own material payoffs. Suppose thesepreferences are commonly known to both players. Derive the Nash equilibrium/equilibriaof the game. Does a player’s best choice depend on the strategy chosen by the otherplayer?
Chapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. 11.1 - Suppose that a and k are both saddle values of the...Ch. 11.1 - Repeat Example 1 for the HDTV game matrix...Ch. 11.1 - Determine which of the matrix games below are...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 1-8, is the matrix game strictly...
Ch. 11.1 - In Problems 1-8, is the matrix game strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16 , the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - In Problems 9-16, the matrix for a strictly...Ch. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - For the matrix game of Problem 31, would you...Ch. 11.1 - For the matrix game of Problem 32, would you...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - In Problems 35-40, discuss the validity of each...Ch. 11.1 - Is there a value of m such that the following is...Ch. 11.1 - Prob. 42ECh. 11.1 - Price war a small town on a major highway has only...Ch. 11.1 - Investment Suppose that you want to invest $10,000...Ch. 11.1 - Store location two competitive pet shops want to...Ch. 11.1 - Store location Two competing auto parts companies...Ch. 11.2 - Let M=abcd (A) Show that if the row minima belong...Ch. 11.2 - (A) Using Theorem 4, give conditions on a,b,c, and...Ch. 11.2 - Solve the following version of the two-finger...Ch. 11.2 - Solve the matrix game: M=112324113Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - In Problems 9-18, which rows and columns of the...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - Solve the matrix games in Problems 19-32,...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - In Problems 33-38, discuss the validity of each...Ch. 11.2 - You R and a friend C are playing the following...Ch. 11.2 - You R and a friend C are playing the following...Ch. 11.2 - For M=abcdP=p1p2Q=q1q2 Show that PMQ=EP,QCh. 11.2 - Using the fundamental theorem of game theory,...Ch. 11.2 - Show non strictly that the determined solution...Ch. 11.2 - Show that if a 22 matrix game has a saddle value,...Ch. 11.2 - Explain how to construct a 22 matrix game M for...Ch. 11.2 - Explain how to construct a 22 matrix game M for...Ch. 11.2 - In Problems 47 and 48, derive the formulas of...Ch. 11.2 - In Problems 47 and 48, derive the formulas of...Ch. 11.2 - Bank promotion A town has only two banks, bank R...Ch. 11.2 - Viewer ratings A city has two competitive...Ch. 11.2 - Investment You have inherited $10,000 just prior...Ch. 11.2 - Corporate farming For a one-time play...Ch. 11.3 - Show that M=1132 is a strictly determined matrix...Ch. 11.3 - Solve the following matrix game using geometric...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 1-6, find the smallest integer k0 such...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - In problem 7-12, solve the matrix game using a...Ch. 11.3 - Is there a better way to solve the matrix game in...Ch. 11.3 - Is there a better way to solve the matrix game in...Ch. 11.3 - Explain why the value of a matrix game is positive...Ch. 11.3 - Explain why the value of a matrix game is negative...Ch. 11.3 - In Problem 17-20, discuss the validity of each...Ch. 11.3 - In Problem 17-20, discuss the validity of each...Ch. 11.3 - In Problem 17-20, discuss the validity of each...Ch. 11.3 - In Problem 17-20, discuss the validity of each...Ch. 11.3 - In Problems 21-24 remove recessive rows and...Ch. 11.3 - In Problems 21-24 remove recessive rows and...Ch. 11.3 - In Problems 21-24 remove recessive rows and...Ch. 11.3 - In Problems 21-24 remove recessive rows and...Ch. 11.3 - (A) Let P and Q be strategies for the 22 matrix...Ch. 11.3 - Use properties of matrix addition and...Ch. 11.3 - Solve the matrix games in problems 27-30 by using...Ch. 11.3 - Solve the matrix games in problems 27-30 by using...Ch. 11.3 - Solve the matrix games in problems 27-30 by using...Ch. 11.3 - Solve the matrix games in problems 27-30 by using...Ch. 11.4 - Outline a procedure for solving the 45 matrix game...Ch. 11.4 - Suppose that the investor in Example 1 wishes to...Ch. 11.4 - In Problems 1-4, solve each matrix game 140012Ch. 11.4 - In Problems 1-4, solve each matrix game. 112201Ch. 11.4 - In Problems 1-4, solve each matrix game. 012103230Ch. 11.4 - In Problems 1-4, solve each matrix game. 120012201Ch. 11.4 - In Problems 5-8, outline a procedure for solving...Ch. 11.4 - In Problems 5-8, outline a procedure for solving...Ch. 11.4 - In Problems 5-8, outline a procedure for solving...Ch. 11.4 - In Problems 5-8, outline a procedure for solving...Ch. 11.4 - Scissors, paper ,stone game This game is well...Ch. 11.4 - Player R has a $2, a $5,and a $10 bill. Player C...Ch. 11.4 - Headphone sales. A department store chain is about...Ch. 11.4 - Tour agency A tour agency organizes standard and...Ch. 11 - In Problems 1 and 2, is the matrix game strictly...Ch. 11 - In Problems 1 and 2, is the matrix game strictly...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - In Problems 3-8, determine the value V of the...Ch. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Delete as many recessive rows and columns as...Ch. 11 - Problems 14-17 refer to the matrix game: M=2101...Ch. 11 - Problems 14-17 refer to the matrix game: M=2101...Ch. 11 - Problems 14-17 refer to the matrix game: M=2101...Ch. 11 - Problems 14-17 refer to the matrix game: M=2101...Ch. 11 - In Problems 18-21, discuss the validity of each...Ch. 11 - In Problems 18-21, discuss the validity of each...Ch. 11 - In Problems 18-21, discuss the validity of each...Ch. 11 - In Problems 18-21, discuss the validity of each...Ch. 11 - In Problems 22-26, solve each matrix game (first...Ch. 11 - In Problems 22-26, solve each matrix game (first...Ch. 11 - In Problems 22-26, solve each matrix game (first...Ch. 11 - In Problems 22-26, solve each matrix game (first...Ch. 11 - In Problems 22-26, solve each matrix game (first...Ch. 11 - Does every strictly determined 22 matrix game have...Ch. 11 - Does every strictly determined 33 matrix game have...Ch. 11 - Finger game Consider the following finger game...Ch. 11 - Refer to Problem 29. Use linear programming and a...Ch. 11 - Agriculture A farmer decides each spring whether...Ch. 11 - Agriculture Refer to Problem 31. Use formulas from...Ch. 11 - Advertising A small town has two competing grocery...Ch. 11 - Advertising Refer to Problem 33. Use linear...
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