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
expand_more
expand_more
format_list_bulleted
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
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Could you please do all parts and provide written solutions , with explanations
Determine the optimal strategy for the situation by representing it as a game and finding the saddle point. State your final answer in the terms of the original question.
In an ongoing price war between Burger Haven (locally owned) and MacArches (a chain), both restaurant managers plan to change the price of a hamburger by 10¢. If
they both raise their prices, there will be no change in their market shares, but if they both lower their prices, the chain's national advertising will ensure that MacArches
gains 6% of the market. Again because of advertising, if Burger Haven lowers their price and MacArches raises their price, Burger Haven will gain only 5% of the market,
but if Burger Haven raises their price and MacArches lowers their price, MacArches will gain 7% of the market. Use this information to decide what the managers should
do.
MacArches
R
%
Burger Haven
%
%
What does L represent?
L represents lowering the price by 10¢.
L represents raising the price by 10¢.
What does R…
PROBLEM (7) Rock-Scissors-Paper game is a two player simultaneous move game where each player chooses R, S or P. It is a fact that Rock crushes Scissors, which cuts Paper which in turn covers Rock; so R beats S, S beats P and P beats R. Winner gets 1 point, loser gets 0 (if they both choose the same strategy; both gets 0). Fill a 3x3 game box with two players’ payoffs in this game and answer the following;
(a) Is there a dominant strategy for Player 1? Any dominated strategy? Answer the same for Player 2.(b) Is there a Nash Equilibrium in this game?(c) If player 1 plays first and then player 2 chooses her action, would you like to be player 1 or 2 in this sequential version of the game? Draw the game tree and describe the backward induction solution (sequential Nash equilibria) in this game.
PLEASE ANSWER ALL THE PARTS!
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...
Additional Math Textbook Solutions
Find more solutions based on key concepts
CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...
Thinking Mathematically (6th Edition)
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th Edition)
If you multiply an odd number by 2 and add 1, is your answer even or odd?
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
In Problems 1-12, use Definition 1 to determine the Laplace transform of the given function. t
Fundamentals of Differential Equations and Boundary Value Problems
The equivalent expression of x(y+z) by using the commutative property.
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
ASSESSMENT Each of the following sequences is either arithmetic or geometric. Identify the sequences 230,193+82...
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Knowledge Booster
Similar questions
- Please don't provide handwritten solution ....arrow_forwardIn a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100.a. Write the above game in normal form. Player 1 Player 2 Strategy A B A $ , $ $ , $ B $ , $ $ , $ b. Find each player’s dominant strategy, if it exists.Player 1's dominant strategy: B no dominant strategy exists A .Player 2's dominant strategy: B no dominant strategy exists A .c. Find the Nash equilibrium of this game. (A,A) (B,A) (A,B) (B,B) d. Which strategy pair has the highest aggregate payoff? (B,A) (A,B) (B,B) (A,A) e. Can the outcome with the highest aggregate payoff be…arrow_forwardThe table below states the payoffs in profits (of millions of tenge each day) to two grocery supermarkets that are rivals in Almaty, Blue Foods and Ladymart. Each supermarket can take one of two courses: Low prices; or high prices. In each cell, the first payoff is for Blue Foods, and the second payoff is for Ladymart. (a) Assume that neither store observes the pricing by the other store, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total profits to the two stores? (b) Now assume that each store can observe the pricing by the other store, and solve the game. Blue Food, Ladymart High prices Low prices High prices 2, 2 0, 3 Low prices 3, 0 1,1arrow_forward
- In a union-management negotiation, the following are the percentages of annual wage increase gained by the Union for various combination of union and management strategies: Management M1 M2 M3 U1 1 3 3 U2 4 2 2 Union U3 3 1 4 U4 3 3 2 U5 3 1 2 Determine the best strategies and values of the game for the union and management respectively.arrow_forwardnot use ai pleasearrow_forwardStudy techniques Your mathematics test is tomorrow and will cover the following topics: game theory, linear programming, and matrix algebra. You have decided to do an "all-nighter" and must determine how to allocate your 8 hours of study time among the three topics. If you were to spend the entire 8 hours on any one of these topics (thus using a pure strategy), you feel confident that you would earn a 90% score on that portion of the test but would not do so well on the other topics. You have come up with the following table, where the entries are your expected scores. (The fact that linear programming and matrix algebra are used in game theory is reflected in these numbers.) Test Game Linear Matrix Your Strategies Theory Programming Algebra Game Theory 90 80 60 Linear Programming 50 90 50 Matrix Algebra 70 30 90 You have been told that the test will be weighted as follows: game theory: 25%; linear programming: 50%; matrix algebra: 25%. (a) If you spend 25% of the night on game theory,…arrow_forward
- Given the following Payoff Matrix: Payoff Table - # of Avg Yards Patriots choses (run) 50% of the time Broncos and choses (pass) 50% of the time Run Pass Run 3 Broncos choses (run) 40% of the time Patriots Pass and choses (pass) 60% of the time 1 Hhow many yards can Patriots expect to gain per 100 plays? Patriotsarrow_forwardd) Consider the following two-person zero-sum game: 3 -2 1) A = (-1 4 2 2 6/ 2 Using linear programming, verify that the value of a game, v = 2 and strategies (0,0,1) for player I and ,,0) for player Il are optimal solutions.arrow_forward6. Solve the following game for optimal strategy based on algebraic method. B1 B2 B3 A 11 12 8. Az 1 -3 -2 A3 6 14 10arrow_forward
- not use aiarrow_forwardQuestion No 4 Solve the following games. Determine the optimal strategy of each player, Saddle point where it exists and value of game. In case all methods fail, only then formulate LPP equations. Solution of LPP is not required. B’ Strategy а. b1 b2 b3 A's Strategy a1 10 15 a2 15 17 3 a3| 4 4 b. B’ Strategy b1 b2 b3 b4 A's Strategy al 0 a2-5 1 3 2 4 а3-2 4 3 B’ Strategy с. b1 b2 b3 A's Strategy a1 3 7 a2| 7 9 1 а3] 10 6 d. B’ Strategy b1 b2 b3 A’s Strategy a1 4 7 a2| 5 a3| 8 8. 4 6 B’ Strategy e. b1 b2 b3 A's Strategy a1 |1 -1 a2|-6 -2 a3|8 -5 2arrow_forwardFind the optimum strategies for player A and player B in the following game. Find the value of the game. (Be sure to look for a saddle point first.) Find the optimum strategy for player A. Choose the correct answer below and fill in the answer box(es) to complete your choice. OA. The game is strictly determined. Player A should choose row (Type a whole number.) B. The game is not strictly determined. Player A should choose row 1 with probability and row 2 with probability (Type integers or simplified fractions.) Find the optimum strategy for player B. Choose the correct answer below and fill in the answer box(es) to complete your choice. OA. The game is not strictly determined. Player B should choose column 1 with probability (Type integers or simplified fractions.) B. The game is strictly determined. Player B should choose column (Type a whole number.) The value of the game is (Type an integer or a simplified fraction.) and column 2 with probabilityarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education