Explanation In a two player game, let R and C be two players where R denotes row and C denotes column. A matrix whose rows and columns are labeled with the strategies of the players is called a payoff matrix where the individual entries represent the payoffs from player C to player R for various moves. Player R would choose a row of the payoff matrix that maximizes R ’s payoffs. The optimal strategy for player R are given as: 1. Determine the least element of each row of the payoff matrix. 2. Choose the row for which the above chosen element is maximum. Similarly, the player C would choose a row of the payoff matrix that minimizes the payoff to R . So, the optimal strategy for player C are given as: 1. Determine the largest element of each column of the payoff matrix. 2. Choose the column for which the above chosen element is minimum. Thus, an entry in the payoff matrix which is simultaneously the least element in its row and the largest element in its column is called a saddle point. For example, Let the payoff matrix for a two player game be A = [ 4 − 6 3 2 ] . Step 1: Select least element of each row

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9, Problem 5FCCE

To determine

The condition for an entry of a payoff matrix to be a saddle point.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 4FCCE

Chapter 9, Problem 6FCCE

Students have asked these similar questions

Question 3. the given integral is convergent or divergent: Use the comparison test to determine whether or not * sin*(x + 1) 7x3 (a) |. d.x g8 + x4 + 1 -dx (b) 2.x4 + x + 1

help me with ab please. please handwrite if possible. please don't use AI tools to answer

-d.x tan x

Chapter 9 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 9.1 - Solutions can be found following the section...Ch. 9.1 - Prob. 2CYU Ch. 9.1 - Prob. 3CYU Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E 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. 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. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - For each of the games that follow, give the payoff...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.2 - Solutions can be found following the section...Ch. 9.2 - Prob. 2CYU Ch. 9.2 - Prob. 1E Ch. 9.2 - Suppose that a game has payoff matrix [102120011]...Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 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. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - 16. Three-Finger Morra Reven and Coddy play a game...Ch. 9.3 - Prob. 1CYU Ch. 9.3 - Prob. 2CYU Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 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. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - In Exercises 13–16, determine the value of the...Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Football Suppose that, when the offense calls a...Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 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. 2FCCE Ch. 9 - Prob. 3FCCE Ch. 9 - Prob. 4FCCE Ch. 9 - Prob. 5FCCE Ch. 9 - Prob. 6FCCE Ch. 9 - Prob. 7FCCE Ch. 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. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 1P Ch. 9 - Prob. 2P Ch. 9 - Prob. 3P Ch. 9 - Prob. 4P Ch. 9 - Prob. 5P Ch. 9 - Prob. 6P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The condition for an entry of a payoff matrix to be a saddle point.

Solution Summary: The author explains that a saddle point is an entry which is simultaneously the least element in its row and the largest element of its column.

Videos

The condition for an entry of a payoff matrix to be a saddle point.

Want to see the full answer?

Chapter 9 Solutions