. Consider the following matrix games. (a) 2 -3 4 -4 -3 1 -1 3 3 2 -1 3 0 2 2 1 " (b) 1 1 9 8 7 4 2 3 -9 2 -8 -6 3 -6 0 -4 6 1 5 -10 (c) 0 1 6 1 5 -2 -8 -6 0 3 (i) Reduce the payoff matrices by repeatedly deleting strictly dominated rows and columns. (ii) Find the saddle point if it exists. (iii) If the reduced payoff matrix found in (i) has two rows or two columns, find the optimal strategies of both players using the geometric method and complementary slackness. (iv) Find the value of each game and state whether the game is fair, or in favor of the row player or column player.
. Consider the following matrix games. (a) 2 -3 4 -4 -3 1 -1 3 3 2 -1 3 0 2 2 1 " (b) 1 1 9 8 7 4 2 3 -9 2 -8 -6 3 -6 0 -4 6 1 5 -10 (c) 0 1 6 1 5 -2 -8 -6 0 3 (i) Reduce the payoff matrices by repeatedly deleting strictly dominated rows and columns. (ii) Find the saddle point if it exists. (iii) If the reduced payoff matrix found in (i) has two rows or two columns, find the optimal strategies of both players using the geometric method and complementary slackness. (iv) Find the value of each game and state whether the game is fair, or in favor of the row player or column player.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider the following matrix games.
(a)
2
-3
4
-4
-3 1 -1
3
3
2
-1
3
0
2 2
1
2
(b)
1
1
9
8
7
0
-6
-4
2
6
-9
1
-8 -6
5 -10 3
4
3
2
(c)
1
1
0
0
1
0 -1
-1 -2
6 -3
1
5
wóŃwo
-2
-8 -6
0
3
(i) Reduce the payoff matrices by repeatedly deleting strictly dominated rows and columns.
(ii) Find the saddle point if it exists.
(iii) If the reduced payoff matrix found in (i) has two rows or two columns, find the optimal
strategies of both players using the geometric method and complementary slackness.
(iv) Find the value of each game and state whether the game is fair, or in favor of the row player
or column player.
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Step 1: Analysis and Introduction
VIEWStep 2: Reduce the matrix on a) by dominance property.
VIEWStep 3: Reduce the matrix on b) by dominance property.
VIEWStep 4: Reduce the matrix on c) by dominance property.
VIEWStep 5: Solve the game a) using LP model.
VIEWStep 6: Solve the game b) using LP model.
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