Assume that two players, Renée and Carlos, play a game with the following payoff matrix (to Renée):
a. Is the game strictly determined? Determine the strategy for each player.
b. What is the value of the game? Is the game fair?
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Finite Mathematics & Its Applications (12th Edition)
- Consider the following game of ’divide the dollar.’ There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Draw the game tree.arrow_forwardConsider the game described by the following table. What is the best response for the column player if s/he knows that the row player will make the Y move? B OA O C ROW PLAYER O There is no definitive answer. X Y COLUMN PLAYER A 4, -1 3, -1 B -1,0 -2,4 C 2,1 0,2arrow_forwardConsider the following normal form of a game. A B C OC OA OD OB (-3,-4) (-1,0) What is the maximin strategy of the row player? D (-2,-5) (-4,-3)arrow_forward
- In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game.arrow_forwardJane draws a marble from a box containing 5 red marbles, 3 green marbles, and4 blue marbles. She receives $2 for a red marble and $3 for a green marble that she draws.If she draws a blue marble, she loses $4. Is the game fair? How many dollars should Janepay for a draw in a fair game?arrow_forwardA game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.arrow_forward
- If a = (-6, 12, -9), b = (2, -16, 18), and c = (28, -14, 3), what is 3. 6+2c? 2 %3D %3D (51, 0, -24) (57, -48, 30) (24, -18, 12) (20, 14, -24) C.arrow_forwardZara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game.arrow_forwardZara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.arrow_forward
- California Lotto officials want to try out a new "big wheel" game. This new game actually consists of two big wheels (spinners). The contestants spin Spinner 1, and then immediately after, they spin Spinner 2 to determine the "multiplier." When both spinners have stopped turning, the dollar amount shown on Spinner 1 is multiplied by the "multiplier" on Spinner 2 and the contestant wins that much money. $100800 20 50 150dp $1000 0.5 135° s5000 100 Spinner 1 Dollars Spinner 2 Multipliers What is the probability of winning the largest amount of money?arrow_forwardtwo players A and B agree to play until one of them wins a certain number of games. P(A wins a game)=p and P(B wins a game)=1-p=q. However, they are forced to quit when A still has a games to win and B still has b games to win. How should they divide their stance to be fair?arrow_forwardNigel and Sofia play the following game. Each of them roll a fair six-sided die once. IfSofia’s number is greater than or equal to Nigel’s number, she wins the game. But ifSofia rolled a number smaller than Nigel’s number, then Nigel rolls again. If Nigel’ssecond roll gives a number that is less than or equal to Sofia’s number, the game endswith a draw. If Nigel’s second roll gives a number larger than Sofia’s number, Nigelwins the game.Find the probability that Nigel wins the game and the probability that Sofia wins thegame.arrow_forward
- 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