GAME OF MATCHING FINGERS Robin and Cathy play a game of matching fingers. On a predetermined signal, both players simultaneously extend one, two, or three fingers from a closed fist. If the sum of the number of fingers extended is even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the number of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin.
a. Construct the payoff matrix for the game.
b. Find the maximin and the minimax strategies for Robin and Cathy, respectively.
c. Is the game strictly determined?
d. If the answer to part (c) is yes, what is the value of the game?
Trending nowThis is a popular solution!
Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
- The Alpha club and the beta club perform service work for the Salvation Army, the Boy's Club, and the Girl Scouts. The Alpha Club performs 50 hours at the Salvation Army, 85 hours at the Boys' Club, and 68 hours for the Girl Scouts. The Beta Club performs 65 hours at the Salvation Army, 32 hours at the Boys' Club, and 94 hours for the Girl Scouts. Tabulate the given data.a. Represent your table as matrix M, a 2 x 3 matrix.b. Determine the Transpose of your answer in a.arrow_forwardRobin and Cathy play a game of matching fingers. On a predetermined signal, both players simultaneously extend 1, 2, or 3 fingers from a closed fist. If the sum of the number of fingers extended is even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the numbers of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin. (a) Construct the payoff matrix for the game. (Assume Robin is the row player and Cathy is the column player.) 1 2 3 123 (b) Find the maximin and the minimax strategies for Robin and Cathy, respectively. The maximin strategy for Robin is to play row The minimax strategy for Cathy is to play column (c) Is the game strictly determined? Yes No (d) If the answer to part (c) is yes, what is the value of the game? (If it is not strictly determined, enter DNE.)arrow_forwardSolve the game whose pay off matrix is given below: Player B B, B2 A, 2 2 Player A A2 -4 -1 -2 3 -3 B, 1.arrow_forward
- Two friends, Khalid  and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. a/ Construct a payoff matrix for the game b/ Is there a unique Nash equilibrium in this game c/ Which strategy should a player use to maximize her chances of winning the game?arrow_forwardRobin and Cathy play a game of matching fingers. On a predetermined signal, both players simultaneously extend 1, 2, or 3 fingers from a closed fist. If the sum of the number of fingers extended is even, then Robin receives an amount in dollars equal to that sum from Cathy. If the sum of the numbers of fingers extended is odd, then Cathy receives an amount in dollars equal to that sum from Robin. (a) Construct the payoff matrix for the game. (Assume Robin is the row player and Cathy is the column player.)  1 2 3 1                            2 3 (b) Find the maximin and the minimax strategies for Robin and Cathy, respectively. The maximin strategy for Robin is to play row  .The minimax strategy for Cathy is to play column  . (c) Is the game strictly determined? YesNo    If the answer to part (c) is yes, what is the value of the game? (If it is not strictly determined, enter DNE.)arrow_forwardThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the results of rolling a fair die 20 times. DATA DISPLAY ROW C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 1 3 2 4 5 4 5 3 5 3 4 2 5 2 2 2 5 3 2 3 1 4 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it appropriate that the same number appears more than once? Why?What is the outcome of the sixth roll?(b) If we simulate more rolls of the die, do you expect to get the same sequence of outcomes? Why or why not? Step 1 (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage