Robin 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 iseven, 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 fromRobin.(a) Construct the payoff matrix for the game. (Assume Robin is the row player and Cathy is the column player.)123123(b) Find the maximin and the minimax strategies for Robin and Cathy, respectively.The maximin strategy for Robin is to play rowThe minimax strategy for Cathy is to play column(c) Is the game strictly determined?YesNo(d) If the answer to part (c) is yes, what is the value of the game? (If it is not strictly determined, enter DNE.)

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Answered: Robin and Cathy play a game of matching…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Robin 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.)
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