Question 2: Three players (A, B and C) play the Card Game. Each player has two cards. The three players have the following card values: Player (A): 5 and 7 Player (B): 4 and 2 Player (C): 8 and 1 Player A starts by putting one card then Player B puts one card then player C puts one card and the game is over. The score of player A (utility value for A) is computed by the following formula: Score(A) = card value(A) - card value(B) - card value(C). The score of player B (utility value for B) is computed by the following formula: Score (B) = card value(B) - card value(A) - card value(C). The score of player C (utility value for C) is computed by the following formula: Score(C) card value(C) - card value(A) - card value(B). a) Construct the corresponding Game Tree. Then find the utility values of all nodes. b) Which player will win the game? c) Show how can the losers make the winner lose the game. What do you note?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Question 2: Three players (A, B and C) play the Card Game. Each player has two cards. The three players have the
following card values:
Player (A): 5 and 7
Player (B): 4 and 2 Player (C): 8 and 1
Player A starts by putting one card then Player B puts one card then player C puts one card and the game is over.
The score of player A (utility value for A) is computed by the following formula:
Score(A) = card value(A) - card value(B) - card value(C).
The score of player B (utility value for B) is computed by the following formula:
Score(B) = card value(B) - card value(A) - card value(C).
The score of player C (utility value for C) is computed by the following formula:
Score(C) card value(C) - card value(A) - card value(B).
a) Construct the corresponding Game Tree. Then find the utility values of all nodes.
b) Which player will win the game?
c) Show how can the losers make the winner lose the game. What do you note?
Transcribed Image Text:Question 2: Three players (A, B and C) play the Card Game. Each player has two cards. The three players have the following card values: Player (A): 5 and 7 Player (B): 4 and 2 Player (C): 8 and 1 Player A starts by putting one card then Player B puts one card then player C puts one card and the game is over. The score of player A (utility value for A) is computed by the following formula: Score(A) = card value(A) - card value(B) - card value(C). The score of player B (utility value for B) is computed by the following formula: Score(B) = card value(B) - card value(A) - card value(C). The score of player C (utility value for C) is computed by the following formula: Score(C) card value(C) - card value(A) - card value(B). a) Construct the corresponding Game Tree. Then find the utility values of all nodes. b) Which player will win the game? c) Show how can the losers make the winner lose the game. What do you note?
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