Game Theory 0-Sum Games

May 11th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

Solution: (a). Column 2 dominates column 1; then row 3 dominates row 4; then column 4 dominates column 3; then row 1 dominates row 2. The resulting submatrix consists of row 1 and 3 vs. columns 2 and 4. Solving this 2 by 2 game and moving back to the original game we find that value is 3/2, I’s optimal strategy is p (1 2, 0,1 2,0) and II’ (0,3 8, 0,5 8). (b). Column 2 dominates column 4; then (1/2)row 1+ (1/2)row 2 dominates row 3; then (1/2)col 1+(1/2)col 2 dominates col 3. The resulting 2 by 2 game is easily solved. Moving back to the original game we find that the value is 30/7, Is optimal strategy is q ’s optimal strategy is (2/7,5/7,0) and II’s optimal strategy is (3/7,4/7,0,0).

Word Count: 567
Showing Page: 1/5
Game Theory 0-Sum Games 1 2 4 3 1 2 2 1 0 1 1 0 4 3 (a) 5 4 MATH 4321 Spring 2013 Assignment Solution 0-Sum Games 2 1. Reduce by dominance to 2x2 games and solve. 6 3 3 5 2 6 4 7 (b) 10 0 7 1 Solution: (a). Column 2 dominates column 1; then row 3 dominates row 4; then column 4 dominates column 3; then row 1 dominates row 2. The resulting submatrix consists of row 1 and 3 vs. columns 2 and 4. Solving this 2 by 2 game and moving back to the original game we find that value is 3/2, Is optimal strategy is p (1 2, 0,1 2,0) and II (0,3 8, 0,5 8). (b). Column 2 dominates column 4; then (1/2)row 1+ (1/2)row 2 dominates row 3; then (1/2)col 1+(1/2)col 2 dominates col 3. The resulting 2 by 2 game is easily solved. Moving back to the original game we find that the value is 30/7, Is optimal strategy is q s optimal strategy is (2/7,5/7,0) and IIs optimal strategy is (3/7,4/7,0,0).2. Reduce by dominance to a 3x2 matrix game and solve: 4 3 12 . 8 4 6 0 8 5 4 * 12 . Then, we use the graphical method in the following. 8 4 * 0 8 *Solution: Note that 5/8xCol2 + 3/8xCol1 uniformly dominates Col3. Therefore, we can delete Col3 to get 4 3 12 0 8 4 6 8 /12 0 8 5 1/ 3 2 / 3 0 4 / 12 Answer: The optimal strategy for I is (4/12, 8/12, 0) The optimal strategy for II

Review from student

Studypool Student
" Excellent work as always thanks so much "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1826 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors